Downloaded Games

That's unfortunate.  When you got the refurbished console back the techs should have done a license transfer of your account for you.  Click on this link to start your transfer and your kids will be able to enjoy access to your games and DLC again.

If you got a refurbished console back from repair with a different console ID, the license transfer should have already been done as stated. But you also would have gotten instructions with the console that you had to "re-download" all your content to re-license it, even if it was already on your HDD. If you didn't follow that instruction, your content hasn't been re-licensed.

If you go to the License Transfer site, do you see one console ID listed, or two (or more)? One should be your current console ID, visible in System Settings on your dashboard. If the current one is the only console ID, all you have to do is "re-download" the games you previously downloaded, and they'll be re-licensed to the current console ID.

If you see another console ID listed, you should follow through with the License Transfer to your current console ID, and then re-download your items. (The re-downloading of items already on your HDD goes really quickly because it is just re-licensing the items.)