Hi Wonder Woman,
I have purchased many different RC helicopters, from toy level helis to full hobby level. None of those are going to work for a 3 or 4 year old.
We DID get my nephew, about 3 at the time, a remote control flying saucer. Somewhat like a helicopter, it could hover, go up and go down.
Here are links to the type of toy I am talking about.
http://www.bycase.com/Remote-Controlled-RC-Flying-Saucer-WHOLESALE-p-16133.html
http://www.thetoybox.com/proddetail.php?prod=44289
http://www.amazonnovelties.com/2007/12/27/air-hogs-vectron-phazer-rc-flying-saucer/
http://www.nextag.com/Toys--zzair+hog+vectronz2700600zB6z5---html
http://www.hobbytron.com/Flying-Saucer-R-C-Toy.html
My nephew had a ton of fun. He ran it up to the ceiling, let it spin around for a while, and then let it crash to the floor. The foam construction means that it does not hurt itself, your furniture or even little fingers. He wold set it upright on the floor, and start flying again.
Good luck!