I think you're trying hard to accomplish what you don't have the power to do. No wonder you feel stressed. You don't have the power to reconcile your husband and your sister.

I would recommend that you go to your nieces graduation without your husband. Make the 3 hour drive. Stay overnight.
Then drive back home the next day. Your husband won't like you going off alone. That is the price he pays for deciding he cannot tolerate being around your sister. He has a right to decide that. He doesn't have the right to stop you attending a family function that you want to be a part of. Accept his decision for what he needs to do for him. Don't miss the family gathering, if you want to be there, which is what you do want and have a perfect right to want. Between now and then, don't try to talk to your husband about your sister. While you're at her house, don't try to talk to your sister about your husband's feelings. She's not going to be interested in hearing that. Accept that - for now - they need to not be around each other. This rift has a better chance of blowing over, if you don't try to force a reconciliation. Enjoy your husband, while you're at home. Enjoy your family while you're on your visit with them. As for you're mom, don't worry about whose side she is on. Resist the temptation to bring up the topic of who disrespected who. That's just adding fuel to the fire. You won't change anyone's mind or convince anyone that they were wrong.

If going to family functions means that your husband doesn't accompany you, then you will end up going to fewer family functions. That's okay. That's the price your family pays for not being able to get along with your husband. You can't split yourself down the middle and give one half of yourself to your family and the other half to your husband. Mostly, you'll be with your husband. Now and then you'll be with your family. Your relationship with one doesn't have to destroy your relationship with the other.

Clearly, a family trip like you went on is something you probably shouldn't do again. Some families like melodrama. You don't have to participate in that. Choose to not feed energy into a feud. I realize it's easy for me to say that because I'm not in the middle of this situation.

Celebrate your niece's achievement on her special day. Let the day you visit be about that. Refuse to be drawn into dumb conversations with your family about who was right and who was wrong. It sounds like your sister has been rude to your husband. It's okay to say to your husband, "I'm sorry my sister was so rude toward you." Your husband has to understand that you cannot control your sister.