Home first, everything else second. That's especially true since you're 4 months out, and any tradeline under six months anecdotally doesn't score as well as a tradeline longer than six months (tradeline seasoning, the anti-AAoA clause if you will).
A ~.7% swing I'm not certain is worth refinancing over for two reasons: first, neither of your credit profiles is being hurt by having an auto loan - if it's being reliably paid on time, that's nothing but goodness going forward in the future. From the sounds of it you're nearing the 2 year mark on that tradeline, if it's in good standing, that's good likely for either you or your wife's score.
Second, if you refi it, while it's nice to have that account paid-in-full, you will have a new tradeline which will hurt your score in the short-term. Also any new tradeline in the year leading up to a mortgage app is probably fair game for uncomfortable questions. Unless you think the auto loan is artificially lowering one of your scores, I would suggest that since the lower of the two is used for mortgage applications, the "damage" you perceive may well already be done as refinancing it won't remove the original tradeline. I don't think the cosigner is treated differently at all, it's not like an AU where the account would come off the AU's report.
That said, for DTI calculations, the aggregate balance isn't used, it's the monthly payment. If you have some extra cash over the downpayment, it might make sense to toss some of that to the car loan: AFAIK if you're within 10 payments of finishing the loan, it won't be counted towards DTI at all. I'm kicking 1K / month to my car payment in order to achieve that by the time I start home shopping around June next year.
