Need help splitting out a shared iPad
You need to make a backup in iTunes of your old iPad and then restore the new iPad with that backup. When you turn on an iPad that is totally new, it askes if you want to restore from backup or start from "new". You want to restore from iTunes backup. 
Guide for backup and restore in Itunes

Once you have all your apps on the new iPad, you can manually delete or wipe the whole old iPad clean.
Here are some useful informations about deleting/cleaning Apple i-devices

Good luck and ask if you have any further problems.

Ps. You need to do a iTunes backup, because if you have alot of data (apps) there will not be space enough on your iCloud free 5GB standard subscription.