I would let him have the kids but let him know that next time, he needs to ask for and not just assume he can have them on your weekends. Something like "H, You can have them this time but please ask me next time you want to make changes to the schedule. It is not appropriate for you to make plans on my weekend without first speaking to me. Next time you do so I will not be so amiable".
I know it's tough. God, I would be in pieces if it were me and can only think rationally because it isn't. You cannot stop him from introducing her to the children. If he doesn't do it this time, he will do it the next opportunity he has. It is only a matter of time. At least this way he cannot blame you (though he probably will find a way to blame you).
Walk the high road. Keep your head up. Handle yourself with as much grace and dignity as you can muster.
Oh, and make plans for the weekend he introduces the kids to the OW. Lots of plans. Preferably with girlfriends, alcohol and lots of dancing.
