I can help you with preventing this problem in the future. You can set your iPod touch so that apps can't be deleted. Go to Settings>General>Restrictions>then where it says 'Deleting Apps' turn that OFF! Anyone with young kids should do this. While you're in Restrictions you might also want to turn off 'In-App Purchases'. Just FYI, you can also set it to limit the volume if you let your kids listen with headphones. Settings>iPod>Volume Limit
I believe if you restore the iPod to factory settings then restore it to your latest back-up, that should work, assuming you've recently backed it up. BUT, I think you'd be better off getting advice from someone else, as I'm not positive about this...