think this is tricky tbh. I would want to know why she doesn't have her dd living with her, but if it was a man then no-one would question why he didn't have custody of the children. It does create a bit of a double standard IMO, not from you in particular but society in general. It is not a given that a woman will always have custody of the children, she could have allowed them to stay with her ex for many reasons - maybe he was violent towards her and she felt the only safe solution was to leave her daughter with him so they would both be safe. Maybe she was the one who left and felt that her daughter would be better staying in her own home in the surroundings/with things she knows so as not to unsettle her too much. Maybe her work commitments prevent her from being there 24/7 and maybe she simply cannot afford childcare. I don't know why some mothers choose to leave their children, but fact remains that some do, just the same as many fathers do. Just because her dd is not living with her I don't think you should be jumping to conclusions that she has a history of violence/mental illness.
I would ask your dh why she doesn't have her dd living with her, but I think there are more fundamental things that will give you an indication as to her suitability as a caregiver to your children. Does she have access to her dd? does she have her dd to stay over on a regular basis, i.e. every other weekend for instance? If she does have unsupervised access t her child, then it is likely that her reasons for not having residency are innocent. if she doesn't, then I would be questioning why not and would then be less likely to want my children staying over there with her.
I would give her the benefit of the doubt for now, and find out suttly without jumping in there with all guns blazing withdrawing access etc. Remember that if you meet someone and you've been this harsh with your ex's new gf, chances are he'll use the opportunity to turn it around on you in the future.