Hi L.,
It is my understanding that ambulances won't take you to the hospital of your choice. Ambulances aren't 'transport services' so they are directed to take you to the nearest facility that will be able to handle your EMERGENCY.
So, if you wake up in the middle of the night in severe pain, bleeding that soaks through your clothing or contractions that are less than 4 minutes apart - call an ambulance and let them take you to the nearest hospital.
For anything else, call your Dr.
Once you describe what is going on, your Dr will be able to give you a good indication of when to report to the hospital. Your Dr will also call ahead and alert them that you are coming which will cut WAY down on your wait to get to your room once you arrive, because they are expecting you.
If your water breaks, once you have the initial loss of fluid (which my understanding is really only about a cup or two of liquid) the rest of it is just a constant 'trickle' so there will be no need to line the seat with plastic - a towel will do fine. A co-worker had her water break at work and just changed her clothes, put on an overnight maxi pad, finished her shift (30 minutes) and then went to the hospital (she wasn't having bad contractions and wasn't around customers or anything that was unsanitary - I don't recommend this lol).
Yes, you are better off in the backseat (even now) because of the airbag. Or just make sure the front seat is back as far as it can go.
Pack a bag now and sit it by the front door, so that all you have to do is grab it when you walk out the door. Don't forget change of clothes for the baby!
You can call a cab (although you might have trouble hailing one...lol)
I would have been more comfortable having a friend take me (thankfully my mom was visiting to help!). You can drive yourself or take the train. Labor usually progresses VERY slowly. I COULD have driven myself, but you don't want to drive if you are distracted, emotional or having contractions that are painful.
If you have already bought the baby seat - put it in your hub's car now. The hospital won't let you leave until they see you have one, so even if you can't get ahold of him to take you, he will at least bring it when he joins you for delivery.
Odds are (old wives tale / myth) that you will go into labor at night (or in the evening just after you eat dinner). So, you should be ok!!!!
How exciting ~ GOOD LUCK!
Good Luck!!!!!