How much is it going to cost you to finish rehabbing this house? Where will you find the money for that? I'm assuming the rent from friends will pay the mortgage payments, but it still costs money to remodel.

How long is she willing to keep the mortgage in her name? What is your long-term plan - to buy her out or to sell the house once it's finished? How you handle things differs depending on your plan.

For instance:
Scenario 1) She agrees to keep the mortgage in her name for two years, and to quitclaim the property to you FOR NO MONEY once you are able to refinance it into your name. You plan to keep the house long-term. Will you be in a position to refinance in 2 years? If interest rates have risen considerably, will you still be able to afford the house at an 8% or 10% interest rate? Is your personal credit rating decent, or crummy? If you spend $20,000 to rehab the house, you might end up with 30 or 35k after selling it, IF she gives up her interest in the house.

Scenario 2) Wife agrees to keep her name on the mortgage and deed but wants to be bought out in two years at 50% of the equity. You spend $20,000 rehabbing the house, room mates carry the mortgage for you. In two years house is worth 200k, you have to come up with $32,500 to buy her out. However, since you had to spend $20k to rehab, and would have to pay realtors fees if you did sell it, you really end up with - zero profit.

Scenario 3) Wife agrees to keep her name on the mortgage for two years, then wants to be bought out at 1/2 of the current (today)equity = $15k. You spend 20k rehabbing and in two years the house is worth 200k. (Values are not projected to go up). After you pay her 15k, your actual profit is 50k - minus 20k invested in rehab = 30k minus costs of selling approx 15k = 15k. That's a whole lot of work for MAYBE 15k. And as someone who just paid 25k last years for a bathroom leak-mold-damage-stripped to studs-new sewer line needed disaster, let me remind you that Murphy's law holds especially true for home remodeling. Will you be able to handle it if you need a new roof, or major plumbing repair, or similar expenses? Is this house relatively new and just in need of cosmetic work, or is it 1960's or older and ripe for major unexpected repairs? Are you experienced at doing this kind of work yourself, or are you expecting to hire it out?

I speak as someone who has earned considerable sweat equity on homes in the past, and has laid tile, built kitchen cabinets out of a flat pack, etc. You CAN earn sweat equity sometimes but it's way harder than most people think - and if you have poor interior decorating taste, you can spend plenty and get NO return on your money.