My man has a 5 year old daughter who comes to our home every other weekend. He divorced about two years ago from his now ex-wife who left him without a word after she landed in hospital following a suicide attempt and a breakdown at a new job. He wasn't allowed to see his kid and she didn't respond to phone calls, text messages or emails. When the divorce papers had been signed he finally got to see the kid again, two months later.
I'm looking for advice as we are worried that her mother is not fit enough to be the main carer.
They have a shared custody but in her eyes that means nothing. We keep finding out very shocking things through her kid and she won't discuss or let us know about. For example she went back to the hospital last year and after that to a women's refugee. Since then she's twice moved homes and won't tell us. Last weekend their daughter came to us and was very unlike herself, talked about always having nightmares, cried and talked nonsense and when in bed screamed loudly for her mom which we've never heard her do before. The day after we find out by accident from the little one that they just moved and she didn't want to. We were so shocked as we would have dealt with her behaviour the day before completely differently if we had known instead of being baffled why she was behaving so strangely.
My guy never asked about the mother's stay at the hospital or if it was true she was at a refugee thinking he was being considerate. He told her what we had heard from the child last fall to clear the air after she had refused to let us have the kid as agreed on and taken her from the kindergarden to ensure he couldn't pick her up. She never denied or commented on it. In fact she never ever tells us anything unless it has to do with what we are supposed to do for the kid or if my guy has to pay for something (which he has always done).
We are also very concerned that she won't ever talk to him through the phone. If something where to happen to the kid while she's with us we can't trust that she will answer the phone if called. Likewise we are scared that if something happend to her while she isn't with us we won't be told until a lot later.
We've very much attempted to sit on the sidelines and hope for the best, never asking her about her personal life or criticise anything. We've secretly been hoping that she was getting better. We've however been thinking for a long time that the lack of communication needs to be addressed and after finding out about the most recent move he decided to send her an email asking for better communication about their daughter's health and environment. She responded with an email accusing him of being abusive, sad and that he was lucky she was even talking to him at all and to not bother her with minor things and that it was definitely not in their daughter's interest that she talk to men like 'him'. She went as far as writing that "men like him" commonly mentally abuse their next partners and children from earlier relationships.
Apart from communication we're also worried about the mother's general ability to care for the kid. She's now moved to her parents (again) where she lives with what I've been told is a very oppressive father. She doesn't work and seems to be incapable to do so and was severely depressed at the time of their divorce. She doesn't seem to have improved. The kid always sleeps with her in her bed which isn't a sin but the mom has tried to tell us to let her do that when she's here. Recently the kid has told us things like that in her home (with mom) she makes the rules and last weekend she told us she wants to work at home in the future. What a bleak future goal for a bright 5 year old who is teaching herself to read and write.

Her mother also behaves to the dad as if his main purpose the days their daughter is here is to please the kid by doing _everything_ she wants to do and not make her do anything she doesn't want to. Like she keeps giving us some ridiculous lists of things the kid enjoys and berated dad in that last email because we sometimes tell the kid 'not now' if she wants something.
After the email we're also very worried that she's painting dad to be a bad abusive person to the kid and people around her.
Finances don't seem to be too hot either and we're worried that this instability in living arrangements and health/bad judgement of mom will hurt the kid in the long run. It's made us wonder if it would perhaps be better for her if her main home would be with us. She starts school next fall.