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To make it simple, it'd be better if she got her paycheck deposited into her own account, and then transferred whatever funds aren't needed to your joint account.
However if that isn't possible, then I'd recommend she deposit the exact amount of funds needed from your joint account into her separate account, but do it the day after she gets paid so the underwriter sees that it's clearly her money.
We decided to go ahead and refinance the vehicle out of both of our names and into just her name (getting a better rate at the same time, whoop!).
So now my new question is... will having my wife make the new payments from our joint checking account still cause problems with the underwriter when viewing my joint bank statements? The debt is no longer in my name, but I'm concerned that he will see that the payments are still coming from our joint account and decide to count that debt against me, even though my name isn't on it, and my wife's pay checks are direct deposited into the same account covering the vehicle payments.
Any advice? Do I need to worry? Should we pay her vehicle notes from her separate checking account?
Since you are using conventional financing, and the car loan is no longer in your name, the payment won't count against you even if the payment is coming from your joint bank account.