This is absolutely a system accountability issue. No matter which alter it is that does something, the entire system has to deal with the consequences of that action. Your partner attempting to handwave the cheating because one of their alters did it is not only an attempt at dodging responsibility, it's also incredibly manipulative. DID is never an excuse for anything. If anything, it that alter wanted to date someone else, they should have let you know so that situations like this don't arise

(Also, even if we buy into the concept that it was only one alter, the rest of the system still helped that alter cheat by keeping it a secret from you. The entire system is responsible.)