It was stated in a January 2020 interview with Alex's neighbor in San Tan Valley that the fight between Lori and Alex happened "about a year ago":
Mom of missing Idaho kids screamed at her killer brother that he brought disgrace on their family' | Daily Mail Online
So it happened around Jan or Feb 2019. And yes, your impression is correct. That was around the same time period when Lori was MIA to Charles and went off with Tylee to stay with her friend April in Kauai. I have long held the same theory as you about the reason for that arguement. I think that fight between Lori and Alex was either before she left for HI and she was angry at Alex because he didn't want to kill Charles (or maybe he had made an attempt we are not aware of and failed?) OR that fight was just after Lori came back from HI and she was angry at Alex because Charles wasn't dead yet. MOO.
I believe that Lori has a habit of lying about her husbands to her friends and family members in order to gain sympathy and persuade them to do what she wants. We saw this tactic when she told her friend April that Charles had been cheating and had turned mean, almost abusive. April says on Dateline that she didn't really believe it about Charles but she also shared she has her own history of divorce. Lori might have used her friend's own history to her advantage to try to gain sympathy (and probably free room and board with April too). We heard from a former friend of Lori's in the very beginning of this case that at one time years ago Lori threatened to lie and falsely claim that Tylee's dad JR was sexually abusing Tylee:
ID - ID - Joshua Vallow, 7, & Tylee Ryan, 17, Rexburg, Sept 2019
Was that possibly a lie she had told Alex to motivate him to attack her ex-husband/Tylee's dad, Joe Ryan with a stun gun in 2007? We don't know what lies she told her family, but I can very well imagine a scenario wherein Lori possibly started claiming that Charles was abusive and told Alex he needed to stand up for her by "taking care of" CV for good. This is all speculation at this point but a scenario such as that would make sense of Lori's purported words to Alex of "you are bringing disgrace on the family" (my paraphrase/not a direct quote). I can't think of any other reason she would have said something like that to Alex at that time. She was either trying to persuade him to do something or was angry that he hadn't yet been persuaded.
MOO.