you should say "no, thank you". Take advantage of the fact that you got your plans under control, the kids will move on with private school and you will have your house and freedom back.
I made a decision in a similar situation to accepter her stay after she asked, and not long after she changed her mind, wanted to leave, and then I was again the one left with no plans, having to rush to try to get things organized for my family. Go ahead with what you have planned, and control over, not her change of mind and behavior.....