I have a somewhat difficult question that I need help to decide what to do.?

I have been talking with someone I met over 10 years ago while I was in college. One day, out of the blue, she vanished, and it was only up until a few months ago I found her and we started talking as friends. Well, as we talked, she found that she was falling deeply in love with me and she did the best to try and tell me and she did. Only bad thing is that the reason why she vanished was because she is terminally ill. We have discussed getting married in April when she comes to visit me so that I can be with her until the end. Here is the problem. She has 3 kids. A 23 year old son who I get along with and 2 teenage daughters who I also get along with. The bad thing is that although they still have their biological father, their mother, who is currently filing for divorce so we can be together, has a husband which the girls call "daddy". Their mom tells me he has absolutely no involvement in their lives. He doesn't spend time with them. He doesn't do a damn thing with them so why do they refer to him as daddy? I talk with them, I do things with them, I do what I can to be a part of their lives, but I am only called by my first name and that gets on my last nerve. I am more of a father than their biological father who walked out on them and this other idiot that wants nothing to do with them. So, my question is, should I continue the relationship with their mother or just end it. The other thing is she is always bringing up that man's name in our conversations. So should I just walk away? At first, she would talk to me about having a baby with me and now she is bringing up all of this stuff about how it would be because she is terminally ill. Up until a few months ago, she said she would do anything and now it's like this. Should I walk away? Thanks for the help.