It takes time.

I decided something you wrote in your OP, I can't care about DHs kids more than he does. I hate to see a kid without a jacket when its cold. I have 2 children, DH has 2 children. DH doesn't enforce my authority to his kids - so they ignore me. Even if they hear me, if DH doesn't say it (or even if he does) they ignore me.

Kids, its going to be cold, grab a jacket when we go to the park.... DH obviously can hear me too. My kids are toasty, DH is freezing because his kids didn't bother, so he gives his jacket to one of them. I use this as an example because it happens once a month at least for the past 7 years. What can I do? Really? Why should I care.

I came to the thought, if the skids act, speak, get grades, grow up to be whatever is good enough for DH and BM - if they feel their children are meeting their expectations - then who am I to change that or step in. It doesn't matter if I totally don't agree with how they are being raised, how they act or how they do in school - if DH and BM are 'proud' then why was I trying to bust my ass to do better for those kids - nobody wanted my help - not BM certainly, not the skids and when I inspected - not even DH. Because to do better for the skids meant more work for DH. Its HARD work and CONSTANT work to be a parent.

So, I focus on my kids, I keep DH informed of my choices for my kids but the skids will only benefit if DH engages with his kids to offer the same. Sometimes he does, sometimes he doesn't - he is never consistent.

Another simple situation, BD15\SD15 - BD gets her hair done by my hairdresser - some fun things, cool cut, temp color etc. DH complains SD's hair is terrible because BM takes her to mutt cuts and SD looks like a Sasquatch (his words, not mine) So I remind DH that he can bring SD to my hairdresser if he wanted to. (remember, I will not do this for him, if I took SD and BM found out - well screw that) DH is too lazy, he says yes yes yes that would be great. OK DH, let me know when you want me to make an appt (I will do that for HIM) Nope nothing, I don't remind him, I don't ask again, I leave it on him. When he brings it up again how SD looks, I say nothing. I am disengaged.

Day to day events, I make meals, I make what I want and enough for everyone - if they complain, DH can deal - if HE wants to make a second meal for them, by all means, I make one meal, I serve, I eat, I clean it - I could care less if they eat or not - that has nothing to do with me.

Laundry - the kids are 9, 10, 15, 15 - I announce I will be doing laundry - bring your clothes and sort them into the piles and I will process them through the machines. If skids ignore me, I proceed without them. If they have no clean clothing, DH can wash them if its out of cycle - you snooze you lose. My kids seem to hear me, my kids bring their clothes down - his ignore me - DH's problem.

This is how I function.