Doesn't Make Sense

Alex absolutely hates her father being around Maddy therefore she fights his help with babysitting or living arrangements even when they appear to be at rock bottom. From what they've shown us of his character, he seems to be a somewhat calm, responsible father who is trying to help her here and there if and sometimes when she will allow it. He often appears to be shown trying to help Sean with his sobriety. During one of the flashbacks it appears that it was the mother who was the violent one, not him...

On the other hand we often see Alex thinking it's perfectly okay to let Maddy remain in the presence of her loud, often foul mouthed mother, who clearly suffers from some type of mental issues as well as having some violent tendencies.

After repeatedly proving she cannot look after herself and has often contributed to Alex's woes, what does Alex do, she invites her mother to move with them? WTF?

This show frustrates me...