There are a couple remedies I heard of; Pumice stick, ajax, comet. You can google for some other ideas. Don't know if any of them really work or not. Also try your local hardware store and ask them, they may have some advice.
Going forward, being how you have little ones that love to stick things down the toilet, buy yourself a toilet bowl auger and use that instead of a snake next time. Just a suggestion.
I'm sure you will be going down this road again. The toilet bowl augers have a plastic shield to prevent the scratching and marking up the toilet bowl.