Normally, I’d suggest you speak to her directly. It sounds like you’re both running into the same issue: who’s the “senior” person.
Since this is your mom’s house, I’d suggest you involve her in this. Let her know from your perspective what’s been going on. Your mom, presumably, sets the house rules:who sits in the front seat, who’s in charge in the kitchen, etc. Time for your mom to take control back. Sounds like your sister is acting like your home is HER domain, therefore, I think it’s time for your mom to remind her it’s her own domain, and how she’d like the two of you to act and share responsibilities and privileges. Ideally, this would have been worked out between the two of you prior to your trip to Eretz Yisroel, but since it was not, now would be a good time as any to re-establish those roles and boundaries and practice living them. Your mom might have to put her in her place. It sounds like you’ve tried peaceful methods.