I think we'd need a lot more information to give you decent advice. Exactly how high is your mortgage? (Better yet, what are your total monthly expenses?) By how much does your salary alone exceed those fixed expenses?
Anyway, I think it would be crazy to spend that $6,000 on your car loans. First of all, given that it wouldn't be enough to close the loan, it won't lower your monthly expenses, which seems to be your primary concern. Secondly, with a family of three, a mortgage, and car debt, I think you need a MUCH larger emergency fund than $6,000!