@Aaron Frances In my opinion, the best way to go is a heloc as stated earlier by another answer. It gives you the flexibility you need without all the closing costs associated with a cash out refinance. I actually recently completed a HELOC on one of my 3 flats with a lender that lends up to 100% LTV (owner occupied). If you truly have the equity you believe you have, that will give you 200K+ of cash available via the HELOC. The best thing is that you can pull only what you need as you need it so that you are not paying interest on the rest. So if you got approved for a 200K line, you can pull 65K at closing to pay off all the debt in your wife's name. The rest just sits there until you are ready to use it. The rate on the HELOC is about 6% (1.9% 9month intro rate) so it will be cheaper than the rates on the installment loans as well if you decide to pay those off. Then whenever you find a second property you can pull the downpayment from the HELOC. The best thing is that you dont pay any interest while you are waiting. It only accrues when you actually pull the cash unlike a cash out.
The only reason i can see to do a refinance right now is if your current loan is an FHA loan and you are looking to free up the FHA to use for another property. In that case you have to see if the numbers are worth it. I refinanced mine out of FHA into conventional prior to doing a HELOC so that i would have FHA available if i wanted to use it again. Also if you go this route, there is nothing that says you have to do a cash out refinance (cash out closing fees are astronomical in my opinion). You can do a rate and term into conventional to keep your payment the same or lower than it is now (especially if you currently have PMI which will be removed based on your equity). Then use the HELOC to pull out the cash you need after the refinance closes. If it appraises like you expect, you can actually use the same appraisal to apply for the HELOC so you dont need to pay for a second appraisal (that's what i did).
Let me know if you have any questions on the above. I believe that is the most flexible way to go about it.