If your ex is feeding his mother that much misinformation, it might behoove you to get to be closer to her, if only to combat his misinformation. I can testify that being the family member of a cheater is awkward. But she is your son’s grandmother. You don’t want her badmouthing you (due to misinformation) when he’s older.
Maybe you could start in a stealth way - “ hey, S2 and I are going to be out your way on an errand, would you like to join us for lunch at Blank Cafe? “
