My DD was 2 years 3 months old when DS was born. Our nearest possible babysitters were my parents 2 hours away. And the scenario you describe happened: DS broke my water at 4:00 a.m.
I called my parents immediately, even before the hospital, to get them a head start. DS decided to move fast and the contractions came on hard, so by 5:00 a.m. we were on our way to the hospital with me moaning and a shell-shocked DD in the backseat.
Was it ideal? No, but we expected this might happen. We had packed "Finding Nemo" for her, and the nurses brought her chocolate milk, and she sat patiently and quietly in my L&D room while I VERY loudly mooed like a cow, trying desperately to stay in control of myself while waiting for some pain relief to not scare DD. She stunned the heck out of me how well she handled it. Besides the occasional side-eye when my moo-ing interrupted Nemo, she didn't seem at all phased. At 7:15 a.m., after getting stuck in rush-hour traffic, my Dad finally got there to rescue DD just as I was getting my epidural.
No one ever told us DD wasn't allowed there (though I made it clear she would be picked up as soon as my Dad could get there.) The anesthesiologist did ask DH to leave the room with DD while giving me my epidural, (if DD weren't there he could have stayed) and I totally understood she didn't want an unpredictable toddler around while messing with my spine. All in all, I was stunned how well DD went with the flow.
Again, in an ideal situation, I wouldn't have DD there, but you do what ya gotta do. Good luck!