Going to see the ENT is the absolute right step. I'm 99% sure that they will tell you that your daughter will need to get her tonsils and/or adenoids removed. In children, the main cause of sleep apnea is enlarged tonsils and/or adenoids. I know this because my nine year-old twin boys were just diagnosed with sleep apnea, and the ENT said that 90% of the tonsilectomies/adenoidectomies she does in children are for sleep apnea. They both had the procedures done this December, and boy, what a difference... no more snoring, no sleeping with their mouths open, no more teeth grinding, and they are so much more alert and calm during the day now, because they are finally getting good, deep REM sleep.
I sooo want to jump on my soap-box and tell every parent I know about this, because most parents have no idea what sleep apnea is (we sure didn't!) After a long struggle with ADD-type symptoms (we had just taken one of our boys to see a psychologist to find out if he had ADD) their orthodontist (of all people!) discovered that they had enlarged tonsils, and asked if the boys were displaying ADD-type symptoms, because sleep apnea symptoms can mimic that.
You will be so happy and amazed at how much better she will sleep once you get the procedure done (if the tonsils and adenoids are, in fact, what is to blame here) The recovery process is a bit hairy (my boys were hurting for about two weeks) but, man, oh man... what a difference. And the fact that you discovered this when she is only four is a blessing too, because apparently, over time, sleep apnea can cause developmental problems, both physically and mentally. I can attest to the psycological symptoms... I had one boy who was totally hyper-active, and one who seemed to be in a total fog, and had short-term memory problems. (It was interesting to see how the lack of sleep affected each one differently, given that they are identical twins). The ENT said that sleep apnea can also stunt their growth (because children do the majority of their growing while they sleep) and that it can even effect the development of their jaw. Because since they are sleeping with their mouths open, the jaw is not held in allignment like it would be if they were sleeping with their mouthes closed, and the upper and lower jaw might then grow at a different rate, causing either an overbite or underbite. Crazy, huh?!?
Sorry to go on and on about this, but I am so passionate about this problem, because if it has not been for our orthodontist, we would have never know this was going on. We didn't see that there was a big problem with the fact that the boys would snore. I now know that snoring is BAD... it means that there is something wrong, some type of obstruction of some kind, and that ANYONE that snores should go to an ENT to be checked, because there is an underlying problem that should be addressed.
Good luck with your daughter! If you are in the Menlo Park area, I can recommend an amazing ENT if you are interested.
-S.