OK, here's my concern: usually children do not drop down to just one nap until 18-24 months. The fact that your daughter has been taking a 10:30 nap, car-enforced, says a lot. Typically that one nap should be early afternoon- to break up the day. I realize this schedule has worked for you in the past....but it has set the stage for your current issues.
Her battles with you are actually nothing new. She's been battling her daddy all this time, & he has addressed the issue by soothing her to sleep in the car. This is your opportunity to set the limits, the schedule, & work on behavior modification...rules & consequences, & to teach her how to self-soothe. If you do it now, then you all will be much happier in the long run. If she's physically battling you now, imagine how much harder it's going to be when she's bigger & older & much louder!
When you look at the #s, sleeping from 9:30pm - 6am is really not that bad. She's getting 8 1/2 hours sleep. Typically, children her age sleep 10-12 hours...but my oldest child (from 18 months to 27 months) slept only 9 hours with a 45 minute nap. His pediatrician said that "bright" children require less sleep & told me to relax! Easy for him to say...hard for me to deal with!!
So, here's some ?s: how much physical activity is she getting? Does she spend time with other children to help wear out that energy? Do you have a structured day - breakfast, playtime, activity time, lunch, story time, naptime, snack time, playtime before dinner, etc.??? My daycare kids all know our routine & repeat it singsong style to the younger children. My fav part is when they say, "first comes lunchtime, then naptime, then snack time, then Mommy time"!!
To aid in the getting the energy out, check with your local library, gym, church, or Parents as Teachers. In fact, Parents as Teachers is an excellent resource for solving issues. They will have media resources to assist you- like the Love & Logic series or the 1-2-3 Method for Discipline. & that's pretty much what your child needs to learn: that her parents are the boss & she is the child who has to obey her parents. Do it now & you'll find Peace!
Ooops, one more thought: on a daily basis, without fail, I use dim rooms & soft music for naptime. I use the same routine day in/day out. A fav blankie, a quiet tuck-in, & I'm out of the room.