I would try to get her down without the car ride- you want to find other ways for her to be soothed and for her to learn to soothe herself.
My son reacts really severely when teething- to the point that I kept him home one day b/c he just stood in the living room and sobbed all morning. We have found that this helps at bedtime:
- Start slowing her down about an hour before you want her to go to sleep
- Have her brush her teeth b/c the brush feels really good on the gums (and it's a good habit to get into)
- On the bad nights (hands in the mouth all day, resistant to eating, drooling, etc), give her some pain meds about an hour before bed time so that it can kick in **Teething really hurts and remember that we would take something if we were in pain!**
- Rock with her for a good 10-15 minutes before putting her down
**We play soft music for my son so that he has something to distract him while he falls asleep**
Once she's laying down, rub her back and don't pick her up again! When my son has a hard time, I quietly go back into his room, lay him back down and rub his back until he's calm.
If she thinks she will score a car ride when she's crying, the behavior is likely to continue well after the pain subsides!