Should I Let IT go?

So my husband and I have been married for 8 years, he has two sisters and two brothers, of all of them he was closest with his older sister and older brother since the day I met him. His sister has been married with the same guy for 16 years up until December of last year. My sister in law and her husband were both out of the country last year in December on a family vacation, well on Dec 24th we are told my sister in laws husband is coming back home early and she is staying behind with their daughter. My husband and I found it a bit odd, but my mother in law was trying to make up excuses so no body in the family would start questioning him coming home with out her.

Well my husband started digging into it because he found it odd as well so since he has a pretty good relations with his sisters husband he called him and asked him what was going on. He told him that they had gotten into an argument and just weren’t getting a long and he thought she was doing fishy thins (cheating) so when he got back home he started looking thru her call logs and messages on their phone bill. Long story short he finds out she supposedly cheated on him and flips out and calls her to tell her she can’t come back to their home and tells her what a hoes she and what not. My husband finds and totally takes his side not knowing if it’s true or not. She states it’s not but my husband doesn’t believe her and for some reason won’t let it go. I hate seeing him ignore his sister and talk bad about her when they were once so close and had a great relationship. I have tried talking to him about and telling him that it’s completely none of his business even if she is guilt and it’s no reason for him to ignore her. We literally argue about it every time it comes up and especially now that she has a new boyfriend. I don’t if I am over reacting and should let it go but I think there has to be something else for why my husband hates his sister so much now. Should I just stop talking to him about it for the sake of our relationship?