She should be the one to find someplace else to hold up over the weekends. Your home and your kids, if she doesn't like it she can vacate on the weekends. JMO
She turned down the idea of a Nanny, why not get a housekeeper to come in once a week instead (I would kill for one
). Also get the kids in some summer all day activities - makes a world of difference, even if it's just one or two days a week or even half day. I fully understand feeling like a single parent 4-5 days a week, it can be extremely draining both emotionally and physically. It does sound like she is feeling desperate and grasping at anything within reach and depressed. I think going to therapy with her would be a good idea.