Thanks everyone for your responses, I really needed some perspective on the situation because I know I am understandably pretty emotional about anything concerning the children.
Offred - I think you're right, she is probably just fine, she has a responsible job etc. so I don't have any other reason to think otherwise. My concern is with him, I wouldn't move in someone that he had never met, I know its different as I have them most of the time but I would put them first no matter what.
oabiti - I'm sorry but I'm glad I'm not the only one! I do think he would keep us apart because of the things he has done, I'm not interested in that, she'll find out what he's like or he'll change, that's not my problem anymore, thank goodness.
Isetan - your message is a big help, pick your battles is a definite mantra of mine but sometimes I forget!
Sammasati - exactly, I don't see why he couldn't have stayed in his flat whilst everyone gets used to each other but that's not his pattern I guess. Its two big things isn't it, Daddy moving house and new girlfriend all at once although I know they're too young to really understand that bit.
MarkRuffalo - that would freak me out! I won't contact her I've made up my mind about that and I think you guys are right on that point.
Gatorade - yes shady, you've hit the nail on the head there, He told me allsorts about his last ex and I'm not a large percentage of it wasn't true now I see it from another side.
I accept I won't get to know her in 5 minutes but as littlejessie mentioned I think it just feels weird that I know everyone who is close to the children so far. I know its his decision to make and if I meet someone I can make those decisions too for myself and the kids. I don't use babysitters just close friends who were known to DH but I do take the point that if we make new friends and have sleepovers etc. that would be the case that he wouldn't know them. I know that I have to accept it as long as DC are happy. I'm not putting up any obstacles, I really want them to have a good relationship with him, I know how important it is and I know how crap he is at thinking of them.
Thank you all for genuinely helping me make a decision and some sage advice for the future, the issue isn't her really, its him, his decision making is still poor, just a year ago he was begging me to stay and now he's moving in with someone else, he's very selfish and does what suits him, I hope I can manage this in the right way for the children's sake that's all.
Cheers xx