Seconding speaking with a lawyer. This will help you understand your options and financial situation.
Also, know that just because she wants to move on that doesn't mean you have to right now. It is hard enough dealing with this revelation, let alone finding a job and place to live at the same moment.
What is best for your kids is to stay in their current situation. Stay in your home. Do not allow her to force you out or sell. There is a significant amount of work to be done and this will take time. Her impulsive desires to run to a new life can wait. She cannot force you to do anything. Your lawyer will help you legally ensure she takes this slowly so all is figured out clearly.
Wishing you strength. You will get through this.
