Bad credit and home buying

Can one with a 580 score and some passed bad choices credit wise (about 5-7 years ago) and SSI as income ever think of owning a home if they have a 100,000 inheritance coming willing to use on down payment? What if their husbands credits about the same but his is also got child support debt from prior marriage but does cash self employed jobs ? And is paying on owed child support. What all debts need to be paid if they’re under $5000? Before this could ever happen or could this happen?