Younger Kids:
Bounce Patrol: a cut above your average nursery rhyme channel, with singing, dancing and some ABC / 123 lessons.
Pocoyo: Very well crafted and entertaining show, slipping in some good lessons.
Yo Gabba Gabba: Such a joy, with fun new topics each episode.
Older Kids:
Science Max / Science Doug
Minecraft redstone tutorials: Mumbo Jumbo
Scratch programming tutorials: Griffpatch
Keyboard / xylophone how do I play this song tutorials
Making stuff (out of cardboard) tutorials
Also, my eldest is 6 and already knows you can get to YouTube via browser -__-
That's a good thing, they won't be completely ignorant with computers. You need to teach them how to be safe, not keep them away from it.
These hyper-restrictive measures are the equivalent of the D.A.R.E program. They will ultimately harm your kids more than any good they could do.