You won't like to hear this, but you are still trying to push an R that X has given no indication he wants. X already set the standard by NOT saying anything on Mother's Day. Although you got a polite response you are intruding in his life and pursuing. Stick to business. If X wants something other than that, he'll let you know. Then you can decide if you want something beyond a business R.
Regarding X's GF:
(1) You might want to try calling her X's GF as a less toxic way of processing information about her. She is no longer the OW. She is his romantic partner.
(2) Anger is certainly a reasonable reaction. It was extremely poor judgment for X to bring his GF in contact with your kids with respect to timing, the lack of communication with you, and so on. Unfortunately, it is his choice to make. You will have zero control over this. The bad thing is that his choices are setting up the kids to be the ones that have to handle your emotional fallout here. Don't let the kids take the hits. NEVER require them to demonstrate love or loyalty to you by having a problem with X's GF or her kids. Unfortunately, it sounds as though they are probably feeling some pressure to do this anyway, as demonstrated by them being wary about talking to you. They should never have been in the position of (1) being the ones to let you know or (2) worrying about your reaction.
Probably the best thing you can do is a strictly business email arranging a time for the two of you to meet with the kid's counselor.
