And those would be some of the "boundaries" that Phoenix recommended laying out. So you don't have to continue to have these altercations.
You're right -- she DOESN'T have the right to know of your comings and goings anymore, other than as they relate to the kids. You do need to tell her a "I will pick up the kids at 9:30" or whatever, and then make sure you stick to it, but if she asks you for an ETA or something after that, just text back "nothing has changed" and then remind her when you see her that by having an affair she has forfeited the right to know your comings and goings.
Good job on the birthday; you played it about right, and i know those are tough.