Hi NDY, I'm just starting to follow your thread. It caught my attention that you have been together with your W for 21 years, and I am married to my W for 22 years. Its the hardest thing we have ever faced, isn't it?
I don't have any special answer for you on your question of whether or not you should kick your W out of the home. But I do know it is not any easier with a separated W who dates (yes, my W also thought at the beginning that just kissing other guys wasn't doing anything wrong).
With a separated W and a son involved you are still connected together. Your W will still do whatever she pleases, but there is no longer the connection of having a home together. And unless there is a lot of fighting, it is better for your s9 if you are all under the same roof. I think for now allowing her to stay in the home is your best course of action, for as long as you can take it.