Updated phone now texts are mixed

Without knowing more details, I cannot know this for certain, but it seems likely that your father's wife is receiving iMessages sent to him, but not SMS text messages. This is the designed behavior – iMessages are delivered to an Apple ID, and if they share an Apple ID, iMessages will go to both of them. The solution is for them to not share an Apple ID.

That said, one can set up a different Apple ID for Messages but keep the same Apple ID for the App store, iTunes, etc. This would alloow them to share purchases, but keep their messages separate from each other.

You can also go into Settings > Messages > Send & Receive and un-check mark the email address that is associated with both of their phones (and Apple IDs). There is a good chance that will also fix your problem.