Is a husband obligated to financially support his wife whom he declared to her that he wants to divorce although she will not move out of their rented home? Or what if she agrees to divorce but is staying in the home until she arranges to move out?
This depends on a number of factors. Who wanted the divorce, what is happening with her wages, etc. If you are seriously considering getting divorced you should ask this to the rabbonim of the bais din that you are dealing with.