If you are going to continue to live in the house and she isn't, instead of buying her out, consider freezing her equity and allowing her to stop making payments. Currently you both have the same equity as you've both paid in the same amount. Calculate that equity.
Equity = Price of house - amount owed on loan
Divide that in half. That's her equity. If that's 25k, she'd have 12.5k and you'd have 12.5k. From now on, your equity is
Equity = Half original equity + amount owed on loan now - amount owed at that time
So if 12.5 is half the original equity (at this moment), you add that to the current loan amount (89k, so a total of 101.5k). In the future, you will subtract out the amount owed on the loan at that time. The resulting amount is your equity. When the house sells, calculate the profit
Profit = Proceeds from house - any fees - amount owed on the loan
That's the amount of money to split. Calculate total equity
Total = Her equity + your equity
Her share is
Her share = Profit * Her equity / Total equity
Your share is
Your share = Profit * Your equity / Total equity
Those two numbers should add up to the profit.
If you sell relatively soon, then you can just split the profit without going through all these calculations.
The point of all this is that buying her out guarantees her a 12.5k return. If you instead just allow her to stop making payments, then you can split the return when the house sells. That is fairer to you than a buyout.
It's reasonable for her to stop making payments, as she no longer lives there and presumably has her own rent payment. You are getting the full enjoyment of the house, so you should make the full payments. But if you do that, you should also get the full equity increase from the ongoing payments. So the split shifts over time.
Another possibility is that you work out a market rent. You make half the mortgage payment plus half the market rent. She pays just the excess of the mortgage over that.
Her payment = Half the mortgage - half the market rent
Then you'd maintain an even split.
This is the equivalent of renting out to someone else. You'd split the rental income and the mortgage payment. Here you're just skipping the rent collection, as you are the one in the house. To be fair to her, you should pay her back rent from the time she moved out. So most likely, you will be paying the whole mortgage payment and she'll pay nothing for some time. If there's still a balance when you sell the house, add it to her share of the profit and subtract from yours.
A third possibility is that you find a tenant and rent it out. You move into an apartment. You use the tenant's rent to pay most of the mortgage. You and your wife split the remaining amount of the mortgage payment. Sell the house with tenant.
Both of you are out of the house. You can rent something in your single price range. You probably have to pay some extra on the mortgage (over and above the rent payment). But neither of you have to pay the full mortgage. Since you say that you want out of the house, this may be the closest to what you want so long as the house does not sell.
You can look for the tenant while you still live there. And look for a new apartment while still living there. You only need to act if you find both.