I have no reason to choose

Blended families are putting your kids last, it's basically telling your kids you don't want them anymore in some cases.
My ex hasn't seen his kids since the new wife had a baby. I've moved several hours away with his two children a couple of months ago and he hasn't realised yet. I'm trying to decide if I should just stay here permanently.

I'm sorry I don't get this post. It's all over the place. I feel there are 2 or 3 different points

I'm in a relationship where we both have kids from previous relationships. No kids together. I agree kids come first but not every time. But yes, the majority of the time. If they are loved, protected, their health and wellbeing is covered then that's as it should be whether you're a single parent, still with their parent or with a person who isn't their parent.
Kids can't and shouldn't grow up thinking they will always be put first in every single situation. I could list many situations where this is true but I would think it's pretty obvious to many of us on here.

I had to sit my kid and partner down about 6 months ago and tell them that they needed to cut their shit. They did nothing but argue for about 3 weeks straight and I constantly had her telling me she wanted to leave and him basically implying that she was lucky he loved me and I lost it at them. I told him I will pick her over him every time, but I will not put up with her being a disrespectful little shit either and they needed to cut the shit and sort themselves or she could go live with her dad and he could find somewhere else to live as well and me and the youngest were going on a holiday to de-stress from putting up with them and weren't coming back. Worked a treat. I dont think they will ever be best friends, but they at least get along now lol.

I'm in an unfortunate position of choosing kids or partner, so is my partner though he doesn't know it yet.
My husband and I have two children each to previous relationships, his daughter suffers from severe anxiety. She is a lovely girl but struggles with every day life and often has melt downs. I do my best to limit how this effects my children, but it does bother them. My husband's ex wife remarried and her husband had to move interstate, she couldn't go as her daughter wouldn't cope with a move. But with the corona virus she hasn't seen her husband in a while and is planning to move to be with him for a while when she can. This means my husband will be having his daughter live with him full time, but if this happens my kids will probably go and live with their dad. So we will both be making that decision soon.

Lots of people choose partners over their kids.

You can't and you don't. I left my ex partner of 11 years because of his kids. I didn't want to leave but nothing was going to change and he wasn't prepared to put in the work to make changes so I left. You cannot expect a parent to put you first above their kids but you also don't have to stick around and come second all the time. I would ask him to leave if this is causing friction, explain that neither yourself or your kids were ready for this and you think he should find somewhere to live at this time.