Wow!!! My sincere respect and admiration to you!! You will make a world of a difference in this kids' lives
Ok, since I was a kid not too long ago, and am working out bitter things with my parents, I'll give you some very practical advice (you probably know many of these things already)
-When kids do something wrong, specially when they know its wrong, dont ask over and over "but why did you do that? why?" its humiliating and cruel. They are kids, not adults, maybe a "you know this is wrong, dont do it again, and these are the consequences" is better.
-Don't tell them they are fat, ugly, stupid... Kids are malleable, whatever you tell them will become true.
-Notice the good things as well as the bad things, it is so easy to just see whatever they do wrong.
-Try and be natural about the mom situation, talk to your partner and see how you are gonna handle it, but pretending she never existed might not be a good idea.
-Be a team with your partner. Your rules should always be the same.
-Clear rules and routine work wonders with kids, specially if they've had a rocky upbringing. There should be a play time, a shower time, a dinner time, a bed time. And a clear consequence for acts (3 minutes in the carpet for swearing, hitting, etc...)
You sound like a very loving, giving person, I'm sure you will be a great parent to these children! Wanting to be there for them is already half the job done
Congratulations on your brave decision!!! And a big hug!