A.D.
HOnest to goodness, the first thing I'd say is that your children will do nothing but benefit from you putting YOU number one on your priority list...which will include removing your three year old from too many extra activities that feed into "your" time.
Try to establish a routine so that at least everyone knows what to expect.
My first son didn't sleep through the night until he was over a year old.
Do you have any close friends you can child swap with so you can do nothign but get some rest? Do you have family members you can rely on? Is dad involved so that he can help out?
One thing someone said to me once that has really stuck with me is that you have to treat yourself as a bank... if you continue to make withdrawals (giving of yourself) without making any deposits -- you just become a shell of a building b/c no true bank can survive that way..... we can't either. :)
Take care of yourself girl! Hang in there.