Firstly, you didn’t mention who was supporting your sister and brother-in-law as well as all the rest of your siblings while they are in Kollel. It would seem that your brother-in-law wishes to be mekayem the mitzvah of being mepharnes his own family. And might feel that if your father-in-law had to go to work to support all the “learners” he did not want to be a burden to him.
In addition, just because he doesn’t learn full time, does not mean he doesn’t learn. It is wrong to judge them and speak about them in negative terms.
You are asking what you should do. Stop listening to Loshan Horan. Do NOT get involved in the exchange. “Forgive me Tatty but I refuse to listen to Loshon Horah about my sister and brother-in-law”. There are two sets of homes and values that this couple were raised in. It seems that your brother-in-law was raised to be a mentch!