You are both residents of the home, even if it is a rental you both have the right to live there, just like the landlord can't kick you out arbitrarily, neither of you can kick the other out.
If you own the home and are married, it is joint property and both of your rights to access are even stronger.
You may go to court and seek a motion for exclusive possession. Unless there is some kind of violence or abuse involved, and you should be be able to back that up with police reports, then the process can take months.
For financial, if the debt is extremely high and especially if the money was spent supporting the family (ie you went into debt when laid off, or used it to pay for child care) then you can make a claim of "undue hardship". This is a very difficult claim, you can't just say "undue hardship" and not prove it. I would recommend going to a accountant or credit counselling service and getting a written report to back up your claims. Show that you have done your best to clean up your budget and consolodate your debt.
Then if your NDI after CS is below the other party's NDI, you have a case. It still remains to be seen what the counter arguments are, and judge has to decide. It is not an easy way out, it is a tough process, but if you are legitimate then this is what you would do.
Meanwhile, both spouses have an obligation to support themselves and the children. The other parent cannot simply not work and claim an income of 0. This is especially true if the child is of school age. You can seek to have a wage imputed, so if they work or not, they would still be considered to have at least that income for support calculations.
If the other parent has full custody, then Child Support is calculated according to your income, and the imputed income won't change that much. However it will affect expense calculations, and spousal support claims.
My personal advice is that your first stop should be a credit counselling service, try to get your finances in as good shape as you can, both so you have documentation and because this is going to be an expensive process no matter what. Then read as much as you can about separation and divorce, and visit legal clinics and/or get a free half hour consultation from a divorce specialist. You will get the most out of a consultation if you do your homework first and know what questions to ask and what details about your situation are relevent. Don't waste time with your lawyer ranting about what a sh*t your ex is, in other words.
