My son is a little over 2 and right around age 2, his sleeping got all weird again. He co-sleeps, so I cannot compare exactly. But particularly since the time change, he's been all off. He typically is up by about 7am, sometimes before, naps either around 10am or sometimes not until around 12-depends on if I keep him busy. Sleeps for 1-3 hours...it's all over the place and then doesn't want to go to sleep now until 9-10pm! He gets those little fits of crazy too! He's be all sleepy and lay down for a minute and then just go nuts!
I've just been experimenting, moving the nap around, moving activities in the day to see if it helps or hurts, playing with the bedtime routine. Seems this might be a 2 year old thing because all the kids in his playgroup are doing similar strange things and dropping naps or not sleeping as much. Best thing I can recommend is to just experiment and see what works best for them both. Talk to them about it to, ask if they are tired, etc.
Hope it improves! We're still touch and go...