Nah that's actually where the Jedi messed up by having Anakin completely cut ties with his mother and then ignoring his concerns when Anakin started having visions of his mother being tormented to death. Luke of all people should know how wrong this approach is considering the fact that he had to make a similar decision between his training with Yoda and rescuing his sister and friends from cloud city. He chose his family and friends which helped him in the end. He's being hypocritical with grogu a little bit but I'm cutting him some slack because unlike his grandmother and his homies on cloud city, Mando isn't in any danger at the moment
While the Jedi should've let Anakin save his mother, that wasn't the main place they messed up. Their main fukk up was training Anakin in the first place.
Anakin was never mentally built for the Jedi life the first place. He's powerful but outside of that he was always a terrible Jedi. Yoda and Mace were right from the jump and shouldn't have allowed him to be trained.
Even if the Jedi let Anakin save his mom he most likely still would've turned to the dark side eventually. He's more concerned about Padme/Shmi than the galaxy and Palpatine could always use that to manipulate him.