I would say that the 10-12 hours for a 4 year old is probably the norm for "most" preschoolers. I do believe that most children are happiest when they are rested.
My daughter is almost 4 and NEEDS her rest. She can be very challenging if she loses even an hour of sleep. I would encourage you to be firm on bedtime. Start your ritual earlier. I don't mean crazy early, but earlier than 9 p.m.
Try starting at a reasonable time, like 8 p.m. This may take some time for her to get used to, but don't be discouraged if she fights you initially. Kids need to see that you are in control, not them. It may also take her an hour or so to wind down. Not every child can "turn off" their brain quickly. But, to encourage restfulness, don't do playful activities right before bed. Encourage quiet activities like books or puzzles.
Set up a consistent (that is the key here) routine and do it EVERY night. Don't give her the choice to stay up and play. Bedtime should be non-negotiable. It is necessary for her health and well-being (as well as yours!).
Consider letting your husband be the one who helps put her to bed. This is still time well spent, and very special to young children. I know that when my husband puts our kids to bed, its a big deal to them (because its only once in a while as he works most nights on the off-shift).
Good luck to you!
Nap time often goes away at an early age. My daughter stopped right around 3. However, I regularly enforce quiet times (at least an hour) to give her a chance to wind down and rest. If nothing else, they can play quietly in their beds, look at books, color...whatever, just as long as its quiet.