Yeah, I'm re-thinking my suggestion of a second dog for your case. Teddy is my first chi and I sometimes forget how needy they can be. When I had my Jack Russell (who was dog aggressive), adding Teddy helped to make her more stable and less needy. But two chis will probably always desire your constant attention, even if they have each other.
Can you maybe work in training sessions where you involve the kids? If you use positive reinforcement (treats and praise for good behavior), even your kids should be able to participate in training. Here's an easy trick:
"Touch" (aka. hard targeting) -- touching a person's open hand with her nose
1. Use your right hand. Keep your hand flat and hold a treat in the middle of your palm. Fold your thumb over it to hold it in place. (It will look a little like you're trying to show someone the number four.)
2. Hold your hand up to your dog and let her sniff your hand. She will naturally try to sniff, lick, or paw at the treat. Whenever her nose comes into contact with the treat or your palm, say "Touch!" and drop the treat immediately. (Try to drop it the second she touches you with her nose.)
-- Repeat 3-5 times until she is familiar with the game.
4. Keep a treat in your right hand as you have been. Next, hold a second treat in your LEFT hand and hide it behind your back. This time, when she touches you with her nose, feed her from your LEFT hand instead of your right. The treat in your right hand doesn't move.
-- Repeat 3-5 times.
5. Finally, remove the treat from your right hand entirely. Hold up your open, empty hand to her. Keep it flat as if you're giving a high-five. Ask her to "Touch." Wait a few seconds for her to figure out the game. If she takes longer than a minute, go back a step and work up to it again. Reward her from your left hand for touching your palm with her nose.
6. At the end you should be able to hold up your open hand an say "Touch." She should touch your palm with her nose, and you will feed her from your left hand. Give lots of praise!
Once you lay the groundwork for this trick, it's a very kid-friendly thing to practice with your dog. Any kid can hold up an open palm. It teaches kids to be confident with dogs and dogs to be confident with approaching open hands. The whole experience should be positive and fun.