Stand *behind* the kid, gently lob the ball forward waist-high, and have the kid hit it. The kid can't help but swing through the ball. (It's also a great drill for eye/hand.)
It's frustrating at first for the kids, but when they start driving the ball they're ecstatic.
Say this a thousand times, just like every coach I ever had did: "Don't swing AT the ball, swing THROUGH the ball. Cut it in half!"
To get kids to follow through, keep yelling "Pose for a picture!" Every kid knows that picture.
This is a great drill, but one they might struggle with considering their age. It's not an easy drill at first, but if they can get it, it will absolutely help with not swinging through the ball. Another drill I like, and a good one to start young, is hitting with a skinny bat and hitting plastic golf balls. (Something like this:
). Won't necessarily help with swinging through the ball, but great for hand-eye coordination and if you have a couple of bats and enough balls, you can break into a few different groups and get a ton of swings in without worrying about kids getting hurt with balls flying all over the place.
When I helped coached my younger brother's teams growing up, I used to just tell the young kids to not be afraid to hit the crap out of the ball. Some of the kids were so worried about making contact they wouldn't hit the ball past the pitcher, but once they started attacking the ball, they saw the results and started swinging like they meant it. Obviously, you don't want them taking wild hacks, but don't be afraid to tell them to put something into it and go after a pitch they like. Sounds simple, but it worked.