Can you teach your little one to nap in a pack-n-play in your room, or a quiet corner of the house? That was what I did when I nannied for two families of young children: one child was dropped off at the other's house. When naptime came around, we opened up the pack-n-play in a finished basement and let the visiting child sleep in there. I know it will be a daily routine, unless you want to leave it set up, but that would at least buy your little guy some space.
And you are right, when there's conflict about naps, that really becomes problematic. Could your older one go without a nap, but with a regular earlier bedtime? We moved my son to 7 pm to bed (he wakes regularly around 5:30 a.m.) at the latest and he doesn't need the nap. Also, offering a quiet play time to lie in bed, listen to a book on tape/look at books or play quietly at something small might be another option, if it works for you. They do need some downtime without a sibling around, for sure.
I hope someone has the perfect idea for you. You sound like you really do love your kids, too--- one of my girlfriends just went through something similar recently, and she's a great mom, so don't be hard on yourself!