Man, I have explained this like a hundred of times. Tremolo is forced to have a crush with Josy. Then is forced to have a crush with Maya. Both of them decide to seduce Tremolo, attract him towards them, in spite of being into a lesbian relationship. Josy at least tell Tremolo that is into a relationship, even if she´s not clear about it. But makes Tremolo believe that this relationship is ending. Maya, not even that. She maintains Tremolo in the Dark, but at the same time she kisses him and try to seduce him. The worst way possible: being ambiguous, like if it were an innocent act. The attitude of the both of them is despicable. Masters of emotional manipulation.
When everything explodes, there is only 3 reasons why Tremolo would like to continue being close with them: he wants to be bigamous, he wants to steal Josy from Maya, or he wants to steal Maya from Josy. So he swallows the pride and humiliation of being emotionally manipulated and continues trying to seduce one or the two of them.
But any man with at least half working brain would cut the ties with them. There is no win in remaining close with one or two girls that you have feelings for, and are into a lesbian relationship. The only reason Tremolo would continue being close to them is not a healthy friendship, but emotional blackmail. M&J have made Tremolo feel bad about leaving them to solve their problems by their own. They have sucked him into their personal dramas and continue asking for his help with Maya´s and Josy´s parents and involving him into their problems to the point that Tremolo is no more able to say "no, let me away from all your problems" without feeling bad with himself. Again: EMOTIONAL BLACKMAILING. That´s not friendship, is a toxic relationship of which Tremolo, plausibly, will be hurt.
Tremolo gets the chance to met the Burkes in private because of M&J problems? OK. Why would Tremolo would like to met the Burkes in private? Actually, it´s another problem for him. Hence the "fuck, fuck, fuck", instead of "great, I´m going to met the Burkes". Proves that, being close with M&J is only a source of problems for Tremolo. That friendship doesn´t work as a narrative resource. Unless DPC´s intentions were create a toxic relationship between the MC and two manipulative drama queen lesbians, to warn the player about the dangers of being involved with that kind of people.
Again: BaDIK would be way better without them. They belong to their onw VN with a linear story and 4 paths: Bigamy, to steal Maya from Josy, to steal Josy from Maya, or a bad ending in which the player ends up alone. That´s all.
