This was immature of my mother, correct?

You are what's called "between a rock and a hard place." Your mother is building alliances and trying to justify her reasons for both cheating and leaving your father. She sees your sister as "more on his side" because she is related to him but not to her. Your mother is being inconsiderate that she is still your blood sister and therefore your alliances are equally divided. But you are fueling the fire by either being quiet and not telling your mother that is is wrong to be insulting to your sister and wrong again in bringing up the issue when you knew it would only rouse your mother. You are the catalist her and your best bet is to stay completely away from the drama of both. Absolutely refuse to be a part of your mother's talking bad about your father or your sister and likewise when you talk to your sister hold your stance firmly and state you will not discuss the issues. Simply tell them that this is difficult for you to be in the middle and they need to respect your right not to be drawn into their verbal/emotional warefare.