I have a good relationship with my dad, but we don't do things just the two of us. If we do something, it's as a family (including my husband and his wife, who for the record is also my mother so I recognize it's not the same thing). BUT, I do have a cousin who had two kids then remarried and had two more and those first two kids treat her husband SO good, just like he is part of the family. They never try to separate her from him.

SD20 definitely pulls a variation of your second scenario, except it's:
"I want you to come see me and take me to dinner at the most expensive restaurant I can find and then take me shopping while I complain about being poor and then give me hundreds of dollars. Don't bring your wife, though- I hate her guts and never want to see her again."

I agree with you. In my case, I have 3 adult SDs and 1 adult SS. They all live in another state, so we don't see them too often, just 2 - 3 times a year. They have all been pretty good to me, but there has been some resistance to the existence of a stepmother by 2 of them. As a result, my husband never spends any time alone with those 2 in particular. He always has me with him so that they will understand that we are married/family. His son gets the most alone time with him because his son is not bothered about it. It works out okay. I understand the resistance, and they are never nasty to me. I'm sure they have petty complaints about me, but for the most part truly like me. I guess I could say the same about them. I have petty complaints about them, but they have been a lot more accepting than I would have expected.

I think the problem is when the SK treats the SP like $hit and dictates things (or tries to) and says the SP isn't welcome.

^^^ THIS. EXACTLY.....

I would have no problem with DH meeting with SS alone or having an occassional outing or lunch without me.

But when SS tries to dictate that I am not welcome, that he doesn't like me or he will be rude to me if I go too then THAT is when I have a problem with DH giving into him.

I don't do things with my dad by myself either. My dd15, I feel has a close relationship with dh (who technically is not her bio dad, but she views him as such since hes raised her since age 2)-they don't go off and do things without me and the other kids.

For me, my Dad seems to think he can't do anything with me or my Sister unless it's both of us together. My Brother cut him off long ago, and refuses to have a relationship with him. It's almost like he feels guilty if he only sees ones of us, we could care less. If he wanted to hang out with just my Sister, I wouldn't have a problem with it, and I don't think she would if the situation was reversed. But I also think my SM questions him on what he does with us and for how long it was when he gets back home.

I don't ever expect to have a normal relationship with him, there's so much space & damage between us. Some done by him, some by me and some by SM.

For my DH, I encourage him to have a relationship with SD, one that doesn't concern me, I'm ok with that. But I wouldn't be ok with SD excluding me to just be mean.

Dh's daughters have never accepted me...not because they care about him, but because he was no longer available to them 24/7 .....a control thing.
Dh has been considering trying to engage his youngest, 20 years old. He told me that "there is no where to go with it". Why? Because she wants "a full relationship with him". Meaning weekends and holidays. And she "has no problem with you". So he says that her answer to his request would be no......because of your wife. Which I had to laugh when dh was telling me this recently. So in the past 6 years, and no contact with his daughters in 4 yrs, I am the problem! She is an emotional vampire, unable to stand on her own two feet. And she pits the adults against each other, by claims of being a victim. I told dh that she and he never had a healthy relationship. It is either enmeshed or not at all. She is incapable of maintaining any boundaries, as witness to even being FB buds with her therapist. The best for me is to stay faw away from that train wreck. Dh is keeping his distance also, but it will end when his daughter whines she wants a relationship. I do not think she has ever had a healthy one. Instead of having friends when younger, she hung out with her father or complained her mother was absent. She never developed mechanisms to self soothe, and now has become a vampire. She does want dh,,but has no conception that it needs to go both ways. Dh exists for her emotional needs only.

"What do you think an close, appropriate relationship between a father & adult daughter looks like?" It sounds more like you are asking if SM should be included in Father / Daughter events. If the SM is still 'engaged', it would be nice to ask if SM wanted to come along to have lunch - never say "Don't bring your wife." I don't get the big hype about Father / Daughter alone time anyway. I spend 'alone time' with several people, my DH is not included, and visa-versa. But there are certain times I know if I left my DH home he would be hurt by it. If I said, "I'm going to a family BBQ and we don't want you to attend", it would be just plain rude. It would give one the impression that there were other issues going on.

In my opinion, a good Father paves the way when the Daughter is still a child for her to grow into a mature, respectful, self-confident, self-reliant adult. If a Father does this his Daughter will not feel like she is in constant need of his time and attention, and she will not see the SM as competition. This is something my DH failed to do with SD. SD was told she was better in all ways than anyone else but at the same time she was not given the hugs or 'I love you's. DH rarely took the time to call her and just ask how she was. So what is left is a Daughter who thinks she is better than anyone else but is an emotional cripple who resents the woman Daddy spends his time with. To this day, it is a very rare occasion DH calls SD, and he is paying the consequences. She never calls or acknowledges Birthdays, Father's Day or Christmas.

I have no objection to DH visiting SD except holidays and our Birthdays. I just won't be with him. Seriously, I wish he WOULD try to do more but he doesn't. No pity for self-inflicted wounds.

This is a great topic and seems to be at the heart of so many issues here on this page.

For me I am now learning that what I view as normal may not be the next person's normal and I am learning tolerance.

For me, my relationship with my father was and still is healthy and there was not a whole lot of special father/daughter time of the lunches, dinners, movies, concerts and that sort of special outing that I associate more with couples. I am now learning though that y views are a bit traditional and am coming to an understanding. I think on the few times it just dad an I did something special, they were prompted by my Mum at times when maybe my confidence was flagging for example. From what I remember one lunch when I started work and a couple of special times like driving me to a dance and saying they were proud of me. The rest was more about playing sport together but mainly with my brother as well. Occasional one on one chats that just sort of happened.

A healthy relationship between father and daughter depends on the people involved. With my parents, my dad isn't my bio but he is my dad, he is the one who raised me and has always loved me. I don't call him anything but dad, never have never will. We are so close it makes my mom, who is my bio mother, mad sometimes. I think its funny. She says I should be on her side but what can I say, I'm a daddies girl! We are even closer than he is with his 3 bio kids. We go to lunch alone sometimes and always talk on the phone. I do that with mom too and we all do things together.
Now, with my SD's and DH and my DD & DS its different. DH does things alone with my DS but not my DD. Prob because DD is only 7 and she can be a handfull at times. And she is a momma's girl too. DH doesn't do things alone with SD19 but he does spend time alone with SD21. At one point in our relationship both SD's told him they didn't want me around, wanted a relationship with him and only him. He put his foot down and told them either both of us or nothing. They finally came around and we have all mended and become close. DH still will not be alone with SD19 though. SD21 moved back in with us a couple months ago and our bond is even stronger. She and I do more together than DH and her. Of course DH works 60+ hours a week. I think DH's reason for not having alone time with SD19 is that she is so much like BM and he knows if he gives an inch she will run with it. We love her deeply but we also know the person she is. I have learned how to deal with that and things have worked out well.
So, like I said, depends on the people in the relationships.

In an intact family I don't think most fathers and daughters would make a point of getting together with mom excluded. Sure sometimes (maybe a shared interest in a sport that mom can't be bothered with for example) and I'm sure it wouldn't be a problem. It is more difficult in step situations. My husband's eldest did demand at one time that he only see her (for things like her birthday, etc...) without me. I was not happy about it. But, step situations are different and I guess it depends on the situation. Even in an intact family if for example a father and his son couldn't get along and stand being around each other, then sure son and mother would probably get together without dad sometimes. But if the son was just jealous and resentful of his dad and didn't want him included in get together s with mom that would be weird and totally unacceptable....don't know if it should really be a lot different if it was his step-dad instead

Maybe in a new step relationship the sm should back off and allow skids time with their dad so they know she isn't there hogging him during their time with him (on scheduled visits etc..) but at the same time as the relationship lengthens, kids grow up and especially if everyone gets along or at least tolerates each other well, not sure what the big deal about alone time with dad is about....