Refinance Car BEFORE or AFTER trying to obtain a mortgage?

Husband is trying to refinance his car, and his bank can DRASTICALLY lower the interest rate. BUT they wont cover the full loan. Leaving about 11K financed, and almost 2K on a separate unsecured loan (because a little upside down on carnote because of high interest rate). Is this NOT GOOD to do before trying to obtain a mortgage in 6 months!? We dont have GREAT credit, but it’s FAIR, and will have 3-4% down (possibly more, anywhere up to 10%), trying to obtain our first home. The lady at the bank, said the unsecured loan, may reduce his credit score temporarily, but he needs it because he doesnt have much credit. I am torn between a FAIR CReport, and a chance to get a house with our money saved, and refinancing his car, risking his score going down (BAD), but him HAVING credit (GOOD). What should we do? All collections and anything like that has been paid off, not much debt at ALL Between both of us other than his carnote. (One credit card of mine, that has a 300 limit, and a $ 50 balance).
With that said, with my small credit card, should I leave the balance on it, or just constantly buy and pay off, buy and pay off, does that really help, or just keeping a small amount on the card, so your debt to income ratio is good. (not maxed out).

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