Tricky one. And I have known at least 5 or 6 examples of this over the years.....
When couples are together for a while, the parents and family grow close. The couple are hurt by the split (usually one more than the other,) but many people forget about the wider family, and how hurt THEY are by the couple splitting.
My friend (let's call her Poppy,) split from her boyfriend a year ago, after 7 years, and his mother and little sister (14,) were devastated. It was his fault, as he cheated, and dumped her for another woman.
She did however, keep contact with the mother and little sister, much to his disgust and anger (AND the new girlfriend's!) Poppy said they were like her own family, and she wasn't about to lose them too.
Even though it pissed off her ex and his new flame, his mother said he has no right to say she and his sister cannot stay friends with Poppy.
After a few months, Poppy's ex and his new flame finished anyway. Whether it was because of Poppy staying friends with his mother and sister she doesn't know. And she doesn't care.
She meets his mother and sister once every 6-8 weeks for coffee. They don't discuss him.
OP, if you want to meet his mother now and again, it's up to you; your ex has no right to say yay or nay!