My Texts Going to my wife's iPhone

Ok, sharing a single Apple ID is not a good idea. Regardless, doing so both of you will see iMessages on either phone that are sent or received to either of you. To stop this, you (or your wife) needs to get your own Apple ID.

As far as SMS text messages, these would be something that you will need to contact your cellular voice provider, as they are the ones that provide you with this service.

Do you both share the same Apple ID? Are these SMS text (green) or iMessage (blue) messages?

Stop sharing an ID. You each need your own.