I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
Contrary to popular belief, two people unfortunately cannot become married simply by living together for an extended period of time. A common law marriage requires that both parties intend to be married to each other (usually evidence through making specific promises to each other), and that they held themselves out to friends and family as married. If the two of you did that, then you'd need to file for divorce. If you didn't, then I'm sorry to say, there's no right to a distribution of assets or spousal support from your child's father.
The law does not specifically require him to provide housing for his daughter (since he could do that simply by having primary custody, such a law wouldn't really help you). What the law says is that he must pay to support his child based on your respective incomes. It's up to the party receiving support to then cover all necessary expenses, including housing. This calculator can help you figure out how much he might be ordered to pay.
If you receive disability income, that amount will be used to determine your contribution to supporting the child. You also have the ability to request a higher amount if you can show the judge that the guidelines amount is not enough to take care of the child, given that your disability prevents you from working. That will require showing your medical records and some evidence regarding your necessary expenses.
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