Bless your heart! First of all, the pregnancy will end eventually and, if you're like me, having an infant that wakes you up in the middle of the night for nursing is NOTHING compared to being pregnant. I'm just EXHAUSTED when I'm pregnant, so I totally sympathize. :)
Have you tried dark curtains? And keeping the room just a tad warmer than you would normally? My kids sleep best when the room is cozy warm and the curtains are dark. :)
Nothing wrong with telling your child, "It is not time to get up, honey!" Or with letting him play quietly in his room, but telling him he will have to wait until you get up to show you his book or puzzles. Alone play is GOOD for your child and getting rest is GOOD for you! As long as your child is safe -- and at three, my son was fine for alone play, and now, as a five year old, entertains his 2 year old sister (who can get out of her bed) and his 8 month old sister (who stays in her crib) in the mornings, while I get around.
Don't feel guilty. :) Congrats on your new addition. And, you know, I think siblings are the best gift you can give your children, and yourself. :) Siblings teach each other a lot of life lessons and believe it or not, will make your life easier and help you to relax a little. :) 3 years is a good span for first and second, or at least it was for us! :) Such a big helper!