Kate, is there a way you can purchase a ticket and use it for someone else later if necessary (or does it have to be purchased in the name of the user)? That might give you the most flexibility and help avoid him feeling pressed or you feeling disappointed if he chooses not to come.
Your situation is a little difficult in that he lives at home, so it makes sense that he would be included in a birthday celebration. Do you normally communicate in person or in some type of writing when you have a business matter?
Either way, I would make it low key, or perhaps make it clear that you are ok with him not coming. "Kids and I are going to XYZ for child A's birthday, shall I book you a ticket?
