If she is this incapacitated now, why wasn’t she in a mental hospital years before she had the chance to harm her children?
She actually was (Sheppard Pratt). The mental illness - schizophrenia, schizoaffective, whatever you want to call the disorder - didn't really start to manifest until after she had Sarah (acc. to Troy and family). We (the public) don't really know a whole lot about the period before Sarah and Jacob went missing, in terms of what specific behaviors were concerning or irresponsible. All we know is that the year prior to the children's disappearances, she was committed to Sheppard Pratt because she claimed to be hearing voices and just other paranoid things. And by his own admission, Troy Turner was no longer in a relationship with Catherine Hoggle at the time of Jacob's birth in 2012. I think by that point he knew something was wrong with her but was ill-equipped to handle it.
Up until the time the kids disappeared, Catherine was platonically living in the apartment with him and the kids, due to the fact that neither of her parents (they are divorced) wanted her to move back in with either of them. There's a lot about her family's dynamic that seems "off" to me, especially when I watched the segment with Lindsey Hoggle saying her daughter had only informed her that she was having a child (the eldest), after giving birth to him (neither Lindsey nor the rest of her family apparently knew that Catherine was pregnant at all with the first child). Anyway, at the time they all seem to have agreed, informally, that Catherine wasn't in a position to have custody. No judge ordered anything and no one went to court to try to legally establish custody. They handled things privately.
That's why they were all taking turns watching the kids and getting babysitters to come over when either the Hoggles or Troy's family weren't able to watch them. In my personal opinion, her parents and the state dropped the ball on this one. I guess the support system (housing, rehabilitation, personal help) for adults living with a serious mental illness must be cruddy in Montgomery County. Her parents must have known their daughter was struggling - she had just come out of residential treatment, wasn't employed, and didn't have a place to live besides under her ex's roof... How did they not step in and help her get back on her feet, stay on her meds, look for work and eventually, obtain partial custody?
Wouldn't that be the logical course of action to take, rather than to basically force her ex / kids' father to shoulder all that responsibility himself? The way I see it, that man was having to take care of 4 "children" incl. an adult who wasn't self-sufficient enough to look after herself, much less the kids. I don't want to judge here, but I think it's borderline inappropriate, what went on and what Troy Turner had to endure without any outside support. It must have felt to him like a weird set-up, to say the least, but he had a good heart and wanted to do the "right thing"... and he sure paid for it.