If the college loan was acquired during the marriage then yes, 50% of the loan can be paid from the proceeds of the house. Can and will are 2 different things. She could argue that this is your debt, and she is not responsible for half of it. Arguing and getting are 2 different things.
During my marriage I helped my ex pay off her student loan. My attorney said I would be entitled to half of that amount back in the settlement. That loan was paid off 20 years ago. I still had the loan document.
Decide what you are willing to pay her in a payoff. Make sure it is something you can live with. If she doesn’t accept it then tell her fine, you will sell the house and you will split the mortgage payment 50/50 till it sells. Put the house on the market at the highest appraised value. Put all this in a separation agreement. Be very detailed as to these conditions. In this market it might not sell for years. If it goes to court a judge would not make you put it on the market at less than appraised value (I think).
A downside to this is you have to deal with your Ex or Stbx for longer than you may want to. Years even.
If she has moved out and you are in the house then you will be living there for half of what you are living there for now. If she stops paying the mortgage then you will have to pick up the payments. In that case, eventually her interest will go to zero.
All of the things I said above my girl friend has been going through. Her house has been on the market for 2 years. She is living in a $400K house paying $750 per month to live there. Of course her ex is pi…ed off, but he screwed up and moved out and then signed a sep agreement with these conditions. He thought the house would sell in weeks because he was so smart and knew the real estate market. Of course she has to deal with him on a weekly basis despite being divorced for 2 years.