This is really what it boils down to.NCP is absolutely allowed to make whatever plans he likes for his children during his parenting time.
Have dad tell the mother no.
You all made plans for your family during HIS parenting time. Neither you, nor dad, need to be making a bunch of drama. "No, sorry, we have plans during my time." End of story.
Have dad ask mom for a detail list of activities so you can plan for the future. Get the info, if it's important to dad. The child won't be the first child to ever miss an event. Honestly, it's likely the parents making a bigger deal than the child will.