There have been some real life situations in which formal members of Families either had only tenuous relationship with their supposed supervisors (Albert Anastasia and his "bosses" the Mangano brothers) or more relevantly to this post, in which rebellious members of one Family get assistance, or support from another Family. If I remember correctly in his book Bonanno claimed that Gambino and Lucchese supported the Gallo Brothers (the model for the Rosatos) in their rebellion against Profaci.

It's not clear if the Rosatos were actual formal members of the Corleone Family or not. All we know is that they feel they were owed something by Clemenza/Pentangeli. IRL Profaci's people did indeed meet with the Gallos and agree to terms-which they broke as soon as was convenient.

As he explained, Michael wanted to buy time to find out who the traitor was and STILL make money with Roth. He couldn't do that if he and Pentangeli were involved in a full scale war against Roth/The Rosatos. That's why he wanted "peace" for a while. He also wanted Roth to believe that Michael would NEVER want to harm Roth or Roth's interests. Now, how he expected Roth to believe this after bum rushing Roth's friends out of Las Vegas is a little bit much to take but I would guess life in organized crime is full of such lying, double dealing and triple crosses.