To get your old iPad apps on the new iPad 2, you will pair it and sync with the iTunes. That's it.
Do a full sync with your old iPad first, then go to the Application list in iTunes and select update all there also. Connect your new iPad and let iTunes do it's thing. You might have to go back and tweak the sync settings to get exactly what you want on the new device, but since it is all on iTunes you'll get it the way you want eventually.
Just wait until you've got the new one set up and are sure you lost nothing before before you ship it to the kids.
You'll want to reset it before you do that. If you give it to them with the free apps installed and all, it will still be on your iTunes account. Make your son-in-law get his own. For the free apps, include the list of things you think they will like on a card. Or help them set it up. Or when their iTunes account is set up use the Gift it feature in iTunes (not sure that works with free apps, but maybe).
Apple is pretty good about maintaining forward compatibility over one or two generations. While you might find a couple apps break, the majority should be fine. The major developers will have fixes out soon after release, if not before.