I don't think that you have any grounds to sue 'her' for the money, unless you can prove that the court order of child support was based on fraud. Even then, the person with standing to sue her is probably your co-owner.
A 'promise' from her to give you back the $8,000 isn't a contract, and likely isn't enforceable in court.
The person that you need to be pursuing for the money back is the person that co-owns the property with you.
In fact, it's probably not even necessary to sue him - if the house is worth (purely as an example) $200,000 and you have $100,000 worth of debt on it, then your equity is $100,000, or $50,000 each - but he's already got $8,000 out so the equity is actually $46,000 his and $54,000 yours. The division can be done that way when the house is finally sold.
Alternatively, of course, you and he could simply 'divy up' the repayments on the refinance loan so that his share of the repayments reflects the extra $8,000 of the refinance money that he got. (Strictly speaking, *HE* got the $8,000, which was paid *on his behalf* to the childs mother)