Final decisions will be legally determined by the separation contract. Guardianship of children and original ownership are factors that lead to not moving.
The person who moves out is usually the person who initiates the seperation. However if the residence is in your name only you have the right to stay put.
In a legal separation, it is whichever individual who wants to move out. If neither individual wants to move, the legal basis is for the filer to move out.
There is not set answer to that. It's something you need to talk about. You and your spouse need to come to a conclusion of who needs to find somewhere else to go. Or you could each live in the home part time.