That's a difficult situation. But it's YOUR gym and YOUR workout time. If you think you can hold it together then I think you should do what you want to do. Just because someone is dead to you doesn't mean you won't see them in person from time to time. It can make you feel bad to see him in person, like a shock to the system, but it sounds like since you live in the same area this might be a fact of life you will need to eventually become comfortable with.

It might also be worth talking to him in person. I don't know what you would say, or what he would say. That also might be the worst thing to do, only you in your situation would know.

Let us know how you do.