Xbox – use Xbox live gold from a different account onto another

I would suggest buying your son a prepaid card. You do have to remember when it runs out and buy another, but they tend to be $10-15 cheaper than buying the same amount of time through Microsoft directly. It's also much easier to stop being a subscriber, since you just don't add more time to the account - no need to figure out how to stop the automatic payments.

In the short term, there isn't much you can do;

You could buy a second Gold account, but there's no way to transfer stats or, more importantly, to share downloaded content and games across accounts. Also, it gets kind of pricey.

In the long term, MS is looking to solve this problem with the XBox One with the introduction of Home Gold Sharing, but sadly, that doesn't help you now with a 360 and kids who, I'm sure, are not particularly patient about such things.

Either way, there's no way to go back in time and split up historical stats and achievements. What's been done on one account has been done on that account forever, and cannot be moved to a different one.