M.H.
Unfortunately, so many of us go through the same thing. I have to say that calling a lawyer is the first thing you need to do. He may give you some specific things you need to provide.
You said that your ex is on SSI for his mental issues? That should be a good start for you. Also, its VERY IMPORTANT that you keep a log book of EVERYTHING that goes on with your daughter and your ex. Write the dates and times that you talk to him and exactly what is said. Write down his responses and your daughters. When he is supposed to take her and he doesnt even call... Write it down. Its way too hard to keep everything in your mental roladex. Keep record of how much time is spent with you versus her father and her reaction of not wanting to go.
Getting HIS relatives to testify on yours and your daughters behalf could also be very helpful. Especially about the "being in the hospital" incident. You may even be able to call the hospital an see if they have record of him being admitted on those dates.
There are so many nooks and crannies when it comes to getting full custody of children. I hope everything works in your favor. Good Luck to you and your family... God Bless