I guess my circumstances with my ex are different. If I were in a bad place and could not provide for my children, I would not send them to be with him (if he were not incarcerated). Though, if he were not incarcerated, we may have a different kind of relationship. So I cannot say for sure. But the circumstances, as they are, if I were in need of a third party to care for my children, I would choose my parents or my sister.
Now lets say that DH and I split. He's paying child support, taking his visitation, he has a stable place to live and a decent income and something happened where I lost my home and was living with a friend, or at a shelter, or on the streets, or in my car... There is nothing that would stop me from placing my daughter with him until I got my self back together.
He is a fit father. Though, he is lazier than me and more laid back about the rules. I think if he were in a positon to parent alone, he would do a good job. They just wouldn't get bathed as frequestly. ;)
BM is homeless. Her life has been going down hill for quite some time. She's not stable and is not showing any signs of working toward stability. DH has offered several times to take SS until she get help, or get her shit together. I would do her a favor, as she would not have to lug a child around to a shelter or worry about if he will have a roof over his head that night. I would also be in the best interest of SS. He would have a warm and stable environment. DH has already said he would do what he could to let BM have visitation. He'd never tell her she can't see SS as long as her requests were reasonable. (Day time, non work hours, etc) And most likely, he'd still provide the transportation. (Since we are 3 hours away.)
No mother in her right mind would WANT her child thrown into this unstable kind of lifestyle. Especially if there were better options for them. So I can only assume that the reason BM refuses is to spite DH. It has been clear since the beginning that it is her goal to make him miserable. She has stated that herself.
I do realize that it is not against the law, or even against our court order, for BM to live in a shelter with SS. I just think its asinine to drag him to that place when there are better options.