Try the darkening shades or curtains it works really well! Also consider putting them both to bed @ 7:00. They are so close in age, they really should begetting the same amount of sleep at night (about 12hrs) and the the two year old should definitely still have one nap in the after noon, around 2:00 but don't let them sleep past 4:00. I would still do a nap for the three year old, if not a nap at least a chance to fall asleep. I call it rest and reading. (If you want more ideas on rest and reading let me know.)
What I do when they get up in the night, is just take their hand,(not carry because then they are getting the reward they wanted) and walk them back to bed and tuck them in with kindness, and leave. Minimal talking the first time if any. and do not hold or rock him. It might take awhile with tiring nights, but eventually he will get it. remember it always gets worse before it gets better. you must do it for at least one week maybe two, to see if it is going to work.
Also you could do a reward system, that if they do lay quietly until it is time to get up, or look at books, or go back to sleep, they can earn something fun in the morning. A small treat or a fun activity, or points for a bigger reward.
Here are some more ideas from some other posts..
Since you have tried putting her to bed a little latter and it didn't work. I would try putting him to bed earlier and or rearranging his nap time. If he is having one nap, it should be close to noon probably right after lunch or an hour after. 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.
The other thing that I do when my kids wake up to early
is go in and comfort them. It might sound funny, but I make sure that I look tired, whisper and not open my eyes all the way. Saying 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".
Make sure they are not your favorite books, because some destruction might occur.
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.