Kingvavy, there is good stuff in this thread. I have been where you are, twice. and I want to share a few additional thoughts.
First, I have a theory that if women begin to judge the men that provide for them, resentment isn't far behind. This is because once they start to feel superior to the man, they resent the fact that they have to rely on him for financial well being. They see it as somehow beneath them. I know that logic doesn't work, but I am telling you it has occurred in both of my marriages and in the marriages of others I know. The answer is to make her earn her keep so she is a contributor to the household. People value what they earn far more than what is given to them.
Second, I think you have to have some absolute boundaries, and she needs to know what they are. Lack of boundaries creates lack of respect, and lack of respect leads to my first point.
Third, never expect a woman to do what is right when it is not in her self interest to do so. Since she is financially dependent on you, if (when) you all split her only means of maintaining her lifestyle will be to take from you. And she will. All she can get. And she won't be fair or honest about it. I know this sounds harsh and jaded but you need to be prepared for it.
I really thought my marriage 2.0 was different and wife 2 hated how wife 1 had tried to milk all the money out of me she could, so I didn't think I ha to protect myself from her. But once the reality of having to support herself hit wife 2, everything changed, and quickly. I wasn't prepared and it cost me some serious dough. If you want to maintain the financial means to do things for and with your kids, you need to prepare yourself for the worst. Hopefully it won't happen, but if it does, you'll be glad you took the precautionary measures. Hope for the best but prepare for the worst!!
Good luck. I know your situation sucks, but it will pass.