Not to mention (implied):
Mom: "I want us to be a family again."
Dad: "Fine--as long as you agree to a divorce first."
I'm not sure why you think she was being honest, nothing we know about her leads us to that. She is playing an angle, maybe trying to improve her bargaining position in the divorce, or protect her image as a mother. She might even have come back simply because her visa expired and the rest is just window dressing.
Her reasons don't have any bearing on the story, and she is clearly not the sort of person who would confide them in others anyway. Not so long ago you were complaining about the story spending too much time on background info.
Excuse me? When did I ever complain that we were given too much information about the characters? I've consistently criticized this story for the exact opposite--that basic information about the characters was being withheld from readers for no discernible reason.
Sure, theoretically the mother may be lying--she may just be out to be a bitch and to boss Uta and her estranged husband around. But what other evidence have we been given for her motivations except what she says?
"Her reasons don't have any bearing on the story." The amount of material in this series that has been defined as having "no bearing on the story" and therefore should be ignored as irrelevant is quite staggering, as are the psychic powers of those select readers who so easily distinguish what has bearing on the "real" story from what doesn't.
I said too much time - you have complained frequently about "lack of focus" when the story has taken time to fill in the history and motivations of characters, and without a context for the reason it would just pushing back your complaint about arbitrary choices one layer with no real change. Why did she become a doctor, why was she friends with Kaoru's mother, why did such a self involved person have children, there is no real ending if you are determined to pick things apart.
As for not telling the truth - try the reactions of the characters that know her - everything Reiichi and Uta have said implies their parents, and especially their mother, are toxic and self-involved. Even Kaoru was worried about Uta going back, did Uta say "Mom isn't that bad", or "give her a chance", no, she said "I've grown up a lot, I can handle her" - not exactly a glowing endorsement.
How many manga have you read where protagonists are transferred between schools "because of their parents' job" no other detail given (promotion, demotion, career change, midlife crisis)? Do you pick those apart too, or just accept the move itself is the relevant part for the plot?