Unable to Sync Movies to iPad
The TV app currently cannot accept video content synced from iTunes. There are 2 explanations:


iTunes itself needs an upgrade to understand that videos should be synced to the TV app instead of the Videos app
Apple has decided that you should not be able to sync video content from the iTunes app at all, only download from iTMS or stream from approved providers.


I think it is the first one. This is a bug which hopefully Apple will resolve soon with an update.

In the meantime, just install the VLC app (free) on your iPad. By connecting the device to your computer and using iTunes to transfer home videos to VLC on your iPad for viewing.