I've been a stepmum for 15 years, since my SS was 3, and now he's 18. It has not always been easy but I'm happy to say that overall it has been a really rewarding experience for me!
My best advice to you is to EVOLVE as the children grow, and be to them what they need at the time they need it. I don't know if you have kids of your own, OP, but a lot of parenting comes down to that anyway.
I became a (sort of) stepmum in my early twenties and saw it as a fun friend/aunty type role to begin with. As my SS grew up and I had kids of my own, that role became sometimes more, and sometimes less, depending on the situation.
Once I had my own kids my perspective changed massively, because of course you see things differently when you're responsible for your own kids.
We had a lot of conflict between the two families when my own kids were small, and I think in hindsight a lot of that was down to my own need to control their environment. Nothing is ever simple when you have to factor in another family's schedule, another way of doing things. It can make you feel, as a new parent, like you're doing things wrong or being judged.
But actually all families are different and that's okay. My biggest piece of advice to you would be to decide on your own boundaries within your house, and not judge what goes on elsewhere. Ultimately, those kids have their own parents who will decide what is okay or not okay.
Things were at times very difficult for us, and for the other family. One thing I've always tried to keep in mind is that they are just people. Regardless of the emotions that are driving you or the kids crazy, remember that they are just people too. Just as it is easy to demonise the step-parent, it's also easy to fall into the trap of demonising the ex-wife. Try to rise above that and remember that she is a human too.
Letting your kids go over to see their dad with his new partner is soul destroying for many mums, try to bear that in mind. It's not personal.
Now that our collective group of kids are all teenagers, me, the dad, and the mum, are all pretty good friends. I think that is entirely possible for step parenting situations, no matter how hard it seems right now.
We have learned between us that some of us are better at certain aspects of parenting and share the load between us. Of course we still argue from time to time (although these days mostly I butt out because it's none of my business... thank god!) The stakes seem lower when the kids are older.
On that note, trust me, things will get better. And even if they don't, it's not a permanent situation. Try to be welcoming and treat your stepkids the way you would have wanted to be treated if you were them. Don't expect them to meet you in the middle: YOU ARE THE ADULT! It's your job to set boundaries and be accommodating emotionally.
My stepson is a lovely young man, he's not the most emotionally available, but he shows his affection in his own way. I try not to be his mum; he has his own. But I hope he always knows I'm here for him whenever he needs me.
OP, I think you're pretty switched on about this already, as long as you figure out what your role is in this scenario, you will be fine. And step parenting is wonderful! And massively under rated. I love it, and am insanely proud of my (step) boy, always!