I am no counselor so this is not meant in any way to be relationship advice. I will leave that to the all those daytime television experts. More importantly I am not an attorney so this is not to be considered legal advice.
And if they have a major financial obligation like a mortgage or even clear title to their house, it can't be divided down the middle.
Someone either gets it or they dispose of it in some way.
Depending on the animosity (and other issues) there can be serious challenges to selling. Obstacles like agreeing on a listing price, ability to show to prospective buyers, open houses, etc.
I have observed cases where an offer is received but one side will not even consider the offer. At some point an offer will need to be negotiated.
I have observed some homes where the occupying spouse refused showings and, when allowed, made sure the property was in less than optimal condition.
I am not an attorney. Disposing of assets like a house is definitely something to discuss with an attorney.
If both individuals are on an existing mortgage then walking away is not the easy escape. Talk with your attorney as "giving the house to the other party" may not free up a mortgage obligation.
The key is seek the advice of an expert attorney and put together a plan. Selling a house at any time is stressful...in this situation the pressures are greater.
However, if selling your house is a first step which you agree on, let me help you.
Although this is a very serious topic I end with what I consider common sense advice.... "Get rid of the house then the spouse!"