I have skim read this thread and see you are probably out meeting this women now so my input might be pointless now but will give it anyway lol
I think i can remember some of your earlier threads regarding your break up with ex etc. The fact that this women doesnt have her dd with her and that there is background info you are not aware puts my back up immediately,it usually takes a fair bit for a child to be kept away from the mother.To have her sleeping with your dc,well i would personally be doing my nut by now about it all.I totally agree that until you are happy with her she should under no circumstances have lone care of your dc,i have volunteered tohelp out at dd nursery and have to be police checked to volunteer,i am a nurse FGS but still have to screened togo help at nursery!
This is a huge reason why i am so glad ex-p is so far away with his lousy gf,and she wont be near my dc,even if they moved closer she would be around my dc over my dead body,she has had 9 children!! 1 of whom passed away in infancy,she has 3 of them with her,the latest to my ex-p,another 2 with their father,another 1 with his father,another 1 with her grandparents and the last 1 with his father in location unknown to ex's gf!!so in a nutshell she had 8 children to 7 different fathers,only has custody of 2 of them,the others are all over the country and he went on to have another with her ! You can see why i am so glad to never have to come up against what you are at the moment rickman!!