Well she thanked her dad and HE didn't correct her and have her thank you as well because he's happy to take all the credit.

He's also fine with stringing you along about this visit. He won't tell his daughter it's a bad time or why.

Your husband is missing a spine.

My suggestion?  "Look, DH.  Do you want me to be a grandmother figure to this child or not?  If you don't that is fine.  There are plenty of needy kids and I can get involved with a volunteer organization to be a substitute GM to one of them.  But if you want me to be involved with this child then I need to actually spend time with him and get to know him.  That means not having your younger daughter around and standing between us. Only you can achieved this.  Let me know what you want and how you plan to move forward.  Until you make some changes I am going to assume that you are OK with your younger daugher preventing me from having a relationship with your grandson."  And then perhaps go ahead and check out the volunteer charities.  It sounds like you have a lot of love to give and there are lots of kids right in your town who would love an honorary granny.  It would take nothing away from your stepgrandson but could add a lot to both your life and that of a local child.

May I ask how old this step-grandson is? 

I can see why the child (regardless of age) would go towards his aunt over a woman he barely knows. Of course, the Aunt who he sees all the time and most weekends. The Aunt and child have a special bond. One that likely has been there since birth and has every little, if anything, to do with you or trying to deny you a role. 

Yes, spending some one on one with the child would help the child get to know you better and perhaps warm up to you and your loving personality. However, Aunt will likely always be the child's preferred go to lady. 

It would be great if there were not long distance between the families because it would give both GPa and you more time with the child. Again, no idea how old this child is, but is there possibilities of having the child occasionally come spend a bit of just one on two time with GPa and you? Minus any other adults. As a grandparent myself, I have access to my grandkids whenever I ask for it. I have gone and picked Gkid up , had him for a weekend or week and then returned child. 

But about that inviting one's self to Dad's? What's up with that. When the invitation to the one daughter's family (SD, her Dh and their child), what gives the other SD the impression she too is free to tag along? As a parent with adult children your DH should be able to spend some time with each of his daughters without necessarily including the other. Sure, holidays are entire family gatherings, but casual invites for a visit do not have to be. The daughter with the husband and child should be able to come visit your home without the other daughter an the other way around. 

While it makes sense for both daughters to be around and participate together when H and you travel to their area (as they both live right there and would be rude to come to visit oe daughter without also seeing the other during the trip) but when it comes to traveling to your home the long distance to visit, there is no reason both daughters must come both at once. 

Now that one was coming and now the other has called and said 'so am I;, and nothing was said at  that moment to tell the uninvited one 'uh, no, not this time, but we'll be seeing in the following month", it is awkward now. The misunderstanding (yeah , it wasn't one) of who was invited is hard to undo without making you appear the reason and the b*tch. How does your DH pick up the phone and say now ' am sorry, other daughter of mine, but my wife doesn't want you to come on this visit because she wants to bond with the child without any interruption and interference from you'. 

The time to have clearly told the daughter she wasn't invited but of course she was welcome to visit on her own sometime was when she self invited herself. 

So yeah, chicken sh*t Dh isn't probably going to fix this an correct the error. Both daughters likely are coming. And it will be his fault for not standing up when the second daughter's call came in. 

But what about doing some rearranging of the visits plans? Give the adult children and the one daughter's DH a chance to go out on the town an do some young adult friendly activities while you and GPa took Jr to the zoo? Or take Jr to some kid friendly activities . I would suggest GPa offer to keep Jr over night while the adults go back to the hotel for the night, but I get the impression they all stay in your home during visits? Since they all expect Dad to foot the bills for their stay and entertainment, I suppose DH could purchase them some 'surprise' tickets to some local event (concert, play, local adult festivity event) and babysitting Jr is on GPa and you. 

In other words, if you can't ditch the uninvited daughter, be clever and finds ways to get rid of all the adults for stretches of time during the visit. 

I think it's likely that this is an avoidance behavior your cowardly H exhibits whenever faced with having to parent his domineering YSD. As Murphy points out, she seems to be the dominant figure in the family, so your H squirms when pressure is applied concerning her. I also can't help but wonder if OSD hasn't already shared the situation with her sister. Kids know their parents weaknesses quite well, and there may be more loyalty between sisters that between daughter and father.

It's generally believed that remarried parents should each handle their own kids, but many people find themselves on this site because they are married to weak/spineless parents who for whatever reason don't want to step up and parent. Sometimes it's more damaging to place unrealistic expectations on a partner than just handling things yourself, but it's tricky to know whether to speak up.

Yours is a delicate situation, make no mistake: wait for your H to handle things and allow frustration and resentment to grow each time he fails to; be direct with your SDs and run the risk that they will resent your interference; or just not pursue a deeper relationship with  SDs and their children at all. Should you decide to speak directly to YSD (firmly, yet delicately with great diplomacy, of course), expect pushback, fireworks, and running to daaddee and her sister in an attempt to triangulate against you. Will your H stand with you when this happens, or cave as he usually does? Will the sisters bond over a common foe, the wicked  interloper SM who's controlling their usually pliable daaddee? You get the picture.

Someone on this site recently compared interacting with SDs  to swimming with sharks, an apt analogy. Your seemingly simple request for bonding time with your H's grandchild could cause WWIII, so proceed with extreme caution and take care of you.

Be direct with SD. Tell her that, while you enjoy spending time with Her, you would like to spend one on one time with SGS and his mom this time and you’ll have her come visit at another time and give her that date for that later visit.

"DH, are you saying SD2 is a complete moron with no reasoning or social skills? If that's what you're saying, ok. If not, tell her this is an SD! and SGS visit to focus on SGS and we will see her the next month."

Also ask him if he has lost his balls in a terrible accident he never told you about.

OK probably not because these sisters are not in their 50s like my sister and me... But there is something about the 2nd sister that makes them permenently jealous of their 2nd birth order. My sister is the same. When she blows into Akld from 'down south' she takes over my parents. I am in the USA and the rest of my family live in NZ. Next week me and my husband and my 2nd sister and her husband are going on holiday/ vacation in 2 different places. My 3rd sister leaves a few days later for Hawaii which leaves #2 who is going to be visiting our parents for a few days and I KNOW she will complain about my parents bathroom not being clean enough, mum and dad should move to their neck of the woods and how my parents (dad cannot travel!) should fly down their way for a week over Christmas.

Basically you are dealing with a bullty. So take this bull and email directly to her "SD2, as great as it is to visit with you we have made special plans for SD1 and her family. So if you are in town it will be great to see you for a meal. But I am sure you will want to catch up with your friends who are in town without hanging out with us again. As for your flight arrival, it is a wee bit early for us. So when you arrive and settle in let us know where you are staying and we can catch up with a good homecooked dinner. If it seems like we aren't spending enough time with you we can always make up when you come for your next visit. I am sure you can appreciate this is a special time for SD1 and her family. We love spending time with each of you and your own families. It is easier for your Dad to individually relate to his grandchildren. So let us know where you are staying and when you are free for my roast lamb dinner with all the trimmings."

Read it to DH and CC him as well in the email so she knows her Dad is onboard with this.

She feels you will talk about her without her being there.She is jealous of her 2nd daughter status. She has taken over her mothers place in the family (is she still around?).

Also she has a good relationship with her nephew but is a wee bit possessive with him.

Your husband is probably like my Dad. His one wish for his birthday was "Just no fights." It didn't happen often due to my sister.DH wants to keep the peace and instead of this being autonomous SD2 took over everything and has appointed herself the family cruise director. Preace is on her terms which holds everyone else hostage.

As for her slight in ignoring you, let it go. But tell DH tells her "Oh don't thank me. SM makes sure all this happens. Without her I would be lost!"