This is a really fucked up story.
Kid was in the custody of mom. Mom has documented mental issues (schizophrenia), stopped seeing counselor, does jot have a stable home situation (couch surfing) and spotty employment......so they take the kid. Cool. I get it.
Dad files for custody, stating the above.
The system's response: Let's give the kid back to the mom so we can then address the custody issue....... WHAT?!
At the very least keep the kid in custody or, I don't know, let the kid "temporarily" live with the parent that has a home, no documented mental issues, steady employment (and another working partner in the home).....etc until you can reasonably decide on mom's issues and custody.....