If you still have the old backup (as in, have NOT done a backup of your iPad to iTunes with the new apps), then you should be able to do a restore from that old backup.
It may be a simple matter of syncing iTunes and the iPad; you don't have to delete the newly installed apps. However, if you want to be absolutely certain, then yes, I'd delete the apps on the iPad and then do a "restore from backup" via iTunes.
I cannot guarantee that the data for the "old" apps will be in the old backup, but I can tell you that people have reported getting all their "stuff" back after a restore from backup. I, personally, have gotten stuff back. But - you have a better chance of getting the stuff back if you use the backup than if you don't. So, there's that...
As always, YMMV.
Good luck.
Marilyn