M.,
Here is what I do for the early morning risers, I go in quickly when I first hear them. Take them by the hand and (It might sound funny, but I make sure that I look tired, whisper and not open my eyes all the way) say something like,
"it is not time to get up yet, it's still sleeping time".
Right now is a good time to be doing this because the sun is on your side.
"See it's still dark outside".
Depending on the persistence of the child, you might get them to lay back down and go to sleep. Or you might have to say,
"Mommy is still sleeping, you can sleep or you can look at some books in your bed and then sleep".
To make sure that the sun is not waking him up, you might want to invest in room darkening blinds or curtains. They are great for summer months especially.
You could also try putting him down 11-12 hrs before he is waking up. Once you can get him to sleep that long again, then you can slowly move his bed time/wake time up by 15 mins every few days till you get to a reasonable time.
I also have a fan in each room. It masks "waking up world" noises. There just might be something that he can hear in the morning that no one else is aware of.
Also some times my kids wake up saying they are hungry. If this is the case, don't feed him a normal breakfast. Just give him a piece of bread and water, and then have him get back in bed and "rest". A lot of the times, just a drink of water will curb that starving feeling.
For the naps I call it Rest & Reading time. They get to "read" look at books for whatever age they are (in your case 2) while soothing music plays (I use classical). When they are finished with their books they lay still and quiet until the music is done. They can get up if they are still awake when it ends. Figure out how long you want her to be in there and time it by the music CD. If they get up before its done or are not being still and quiet then I start the CD over and Rest & Reading time is extended. Either way I get some quiet time and they do too, weather they sleep or not. And if it is extended, it doesn't bother me one bit! :)
I would keep trying to at least have some down time for him he needs about 14hrs of sleep in 24 hours.
Good luck
E.