My parents are still married and I have 3 siblings. My siblings and I all try to spend time alone with our parents (one or both) when we can. It isn't personal, but we still want that 1-on-1 time.

My DD has 3 siblings (my exDH’s and SM’s kids) and she most certainly spends time with them wherever and whenever she can. They are close.

As about step siblings I’d say I would not expect the kind of closeness or desire to spend time with.  My DD would spend time with SDs if they are around but neither would   seek it out.

Regularly spending time with just a parent is rude but it doesn’t mean it should be never happening. My DD just left after her visit from out iof state and we didn’t drag my DH with us to go bra or swimsuit shopping with us. I don’t believe in being attached to the hip to ones spouse 

Yes for all three. DD doesn’t think of skids as her siblings and doesn’t like spending time with them. DH spends time with his father without inviting the stepmom. DH does stuff with skids alone because I refuse to eat or hangout with sloth skids.

I really think the motivation for why the seperation occur matters.
And on the whole, yes, I do think it is ok.

I grew up in an "intact family".
My sister is 8 years older than me.
She detested being around me for the most part.
We were always at different stages of development in our childhood years and I think my sister viewed me as a "nuisance".
There was no "step" element but still I wasn't her favourite "play mate".
I think when we have a step element, we automatically assume that it is the reason kids don't want to be around each other.
It may just be an age related element.
It may be that the two children in the same house have fundamentally different personalities - like my sister and I do.

As an adult, I would call my Dad and ask him to lunch.
I did not invite my Mom.
And neither did it even occur to me to invite her - I wanted to spend time with my Dad.
I would call my mom and invite her to lunch - and not ask my Dad to go along.
My aim was to spend time with my Mom.
Sometimes I just wanted to see the one parent and not the other.
(They were married and living in the same house.)
Sometimes I would go out with both - invite them both to lunch or out for the day.
And yes, in all those instances, it never ever occured to me to invite my sister along.
Why would it?
If she wanted to see my parents, she could invite them out on her own.

My mother or father did not have the "dismissive" step kid excuse for what I did.
It was a "normal" thing and neither suspected - rightly  - that I had any underhanded motives.
My actions were not aimed at excluding anyone - even though looking at it now through your eyes,this is exactly what I was doing.
I think that with adult children, their is a need for the child to see a particular person,
Excluding others is not necessarily done for a malicious reason.
Excluding others in a step situation, may not be for "step" reasons.
Even if I was a step kid, I would still have invited out the one parent  - to  the  possible dismay of the step parent.

By the same token, there should not be something stopping you from inviting the adult kid out with both you and DH and your kids.
For me, it cuts two ways, even though a skid inviting a parent out can seem particularly hurtful and a personal slight aimed directly at you.

Between doing things without certain family members and purposefully excluding certain family members.  I think all too often in stepfamilies, purposeful exclusion occurs, and it's hurtful.  

For me what stands out is just the travel time... I don't know that DH should be invited to travel super far without even just a courteous invite to you... As said above, purposeful exclusion isn't okay, spending time individually is, but requesting that certain family memebers are not allowed to be present is much different.

What does your DH say? Is he willing to travel to see them alone even though you're not welcome? If they had phrased it as "we just want some time with you dad. Can you come to visit us?" vs. "we only want you, don't bring so and so." I think those are two VERY different situations. One is expressing a stark unwelcome, while the other is just trying to connect with their dad. I hope, if they're making it a stark unwelcome, your DH lets that know that he doesn't have interest in going places his wife isn't welcome (not that you HAVE to go with him, it's just the principle of you not being allowed)

Is it "okay" for adult children from the "first family" (for lack of better word) not want to spend time with their siblings from the second family?

Does it make a difference if there is a huge age gap? Siblings weren't raised together? Does it matter if it's step or bio siblings?

Is it "okay" for adult child to ask parent to spend time with them (even if it requires traveling) without younger siblings or even without parent's current spouse?

Yes to all three for me.  I see my dad all the time without my younger bio brother and vice versa. 

The third bullet is only a bit more complex and only when it relates to whether the current spouse is included.  Depending on the travel and reason for travel, excluding a current spouse may or may not be acceptable in my books.

I think it's completely normal.  Also depends on age difference and how much time they were raised together.  Even in intact homes sometimes the kids want to spend one on one w/their parent.  Nothing exclusionary about that. 

It depends if they want a relationship with that person.

My youngest and I were discussing family and relationships. He was lamenting about having to spend time with DHs family, who aren’t even related to him. Here’s what I told him.

If you want a relationship with someone you need to spend time with them, get to actually know them. Once you know them then you can decide if you like them and if you want to spend your free time with them. As you get older family becomes more important. It doesn’t matter if you are related by blood or by marriage. It’s much better to have lots of people who love you and who you love around. It makes life easier knowing that family is there for you. 

Theyll only be there for you if you have a relationship with them. One that’s been built up of years of being together and family time. 

If, after spending time with them you decide you don’t want a relationship then no, you don’t have to spend any time at all with people you don’t like. Even family.

As a jaded stepper,  I feel motive needs to be considered, especially if the skid is an adult. Is there a hidden agenda? 

Ideally, skids wanting to spend time with our bios is desirable and a sign of successful blending. But as a responsible parent, or course you have to be careful.

When YSD came to live with us, she was 14. Not only had she been out of DH's life for six years, but she had two older, somewhat trashy stepsisters (BM's other daughters, who had nothing to do with their psycho mother) who hadn't seen her, either. we arranged some visits, but ultimately had to stop allowing them due to illegal activity occurring in one stepsis'  home. In hindsight, we should have insisted on happen in our home, gradually over time. The whole experience was a draining pita.

I think with all of DH's children, the age gap and growing up mostly apart just makes them not so close.  From BM1, he had SS35 and SD33.  With BM2, he had SS15 who lives with us.  As far as I understand, SS35 was already almost married and living with his now wife when SS15 was born.  There was also bad blood between SS35 and BM2.  BM2 helped to "raise" DH's older children and she was just as bat crap crazy back then as she is now.

At some point, when DH and BM2 lived in Cyprus, SD33 lived with them for awhile.  SS15 was quite young, I believe between 2-4 years old, so SD looked after him a lot.  Especially when their marriage was deteriorating, SD told me she looked after SS nearly 100%.  Because of this, SD is way closer to SS15 than SS35 is to him.

I'm lucky in that the older skids have never had a problem with me.  Everyone hated BM2 so, when I came along, everyone basically cheered.  So I'm always included in outtings and parties, etc.  Though the SS's aren't that close but SS15 would love a shoe if you called it family.

So I lucked out with older skids being awesome.  Still stuck with a psycho sl*t GUBM2 but at least she lives in a different country