Um, Fullerton? What's in Fullerton?
There are reasonably priced hotels near Disneyland. Plenty. Within walking distance. So you can walk back to your hotel midday and nap if you want, then come back and stay late for the parade and fireworks.
If you drive to Disneyland, you will have to plan to avoid rush hour. Which actually lasts for 2-3 hours. And there is some traffic all the time, not just during rush hour. It's no fun at all.
Stay in Anaheim and save your energy for the park. My kids and I stayed at the Alpine Inn for less than $100/night. Even tho my mom lives 25 miles from Disneyland and we could stay there for free. Because I didn't want to spend an hour in traffic boxed in by large trucks and aggravated drivers, or worse in no traffic, trying to run me off the road at 80 miles an hour on my way to the "happiest place on earth". Good luck finding a hotel and have fun at Disneyland.