I feel very passionately about this, based on my experience with DD. My water broke very suddenly at 35 weeks and I immediately freaked out and went to the hospital. I was terrified that the baby was too early and I forgot to stop and breathe. The other problem was that there was a huge snowstorm that night and I didn't want to get stuck at home or on the freeway. You probably won't have to deal with that!
But I really, really wish I had taken a few moments to gather my thoughts, take a shower, breathe, take a picture of my fully pregnant self, etc. before dashing out the door in tears.
I spent 12 hours in labor, and I wish about 8 of them had been at home in my bed, where I could have rested instead of being freaked out in the hospital. (But again, the storm made that impossible.)
Anyway, I always say wait until you need to leave, and enjoy whatever time at home you have. Emotionally you will be much better off if you leave calmly rather than in a big chaotic rush. But I would definitely call the MW and let her know what is going on.
(This is more for others, not for you, Gina, since you have BTDT several times and know how your labors usually go.)