If you want to keep the account on there just go to messaging in setting and have receive at only the phone number on each and it should solve it. My husband and I have same apple if don't have problems.
Kitty, that's a great question and Gina's suggestion is a great solution! This setting would be under Settings, Messages, Send & Receive. Make sure the email address used for the Apple ID is not selected. In addition, go to Settings, iCloud, and uncheck anything else that you don't want shared between the two devices. If you do decide to create a separate Apple ID for one of the devices, go to Settings, iTunes and AppStores to logout and create new account.
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