At 2, DD slept 7-7 with a 1-3 hour nap. At 2.5 she wouldn't sleep until 10pm if she napped even 10 minutes so we dropped the nap. She then went back to 7-7.
DS is 2y8m and for the last few months has been staying awake so late. We tried dropping the nap. Some days he's ok, others he just falls asleep randomly at 3-4pm, so clearly not ready to drop it completely yet. But on days where he doesn't nap he is still awake til 9pm!
He is in a big bed and has things in hus room he can do. He is usually happy to be put to bed at 8pm. He then gets up, turns the light on and plays quietly. Some nights he just puts himself to sleep. Others he calls out after an hour or so and asks for milk. So I give him a cup of milk and he falls asleep quickly after that. (Yes, he also gets milk before we initially put him to bed.) He is up around 6.30-7 am.
So we're accepting the late sleep time but don't let him rule our life late at night. Like you, I can't be doing housework at 11pm!!