Traveling 37 weeks pregnant?

Elisabeth
I'm supposed to travel from California to Utah and back with my husband and mother-in-law in three weeks because my sister in law is throwing me a baby shower (a lot of my family and my husband's family lives in Utah). I feel really nervous about driving what will be a total of 26 hours, a lot of which will be through the middle of nowhere, just three weeks before my due date. What if I start to go into labor and we're nowhere near a hospital?
I'm nervous to address this with my mother in law because I know she and her daughter have put a lot of work into this shower. I don't want to disappoint them. But I'm already in excruciating pain at 34 weeks and I just don't think my body will be able to handle the trip when I'm 37 weeks. My MIL always had really easy pregnancies too, so she doesn't think anything of making the trip so close to my due date.
What would you do? Advice please!