Try going into your iPad settings for Messaging, tap on "Send & Receive" and look at the entries for "You can be reached by iMessage at:" If your phone number is still designated as a valid address to send an iMessage to, then your wife's texts will be routed to the iPad. For your iPad, you should just be using an e-mail address for iMessage, so uncheck or remove any reference to your phone number.
Then, have your wife go to her Contacts entry for you and tap "Send Message" to initiate a new message thread. She might see various choices besides your phone number, so have her select your phone number and send a text to that. That should do it, but if you have past messages between each other then those might be based on your e-mail, which means it will appear she's sending a "text" to you but it will go out as iMessage because of the dialog history.
Apple offers a ridiculous "solution" for a problem they created.
I recently switched from iPhone to a Samsung Galaxy S5. It became clear shortly after activation that I was not receiving texts from other iPhone users.
After a quick search it became clear that the issue was with iMessage. That is, otheriPhone users were sending me texts via iMessage. While this problem appears to be widespread and my search revealed a class action lawsuit against Apple for this issue, there were no viable solutions.
In a nutshell, Apple support told me the ONLY fixes to this issues were to 1. Have all of my contacts delete our text thread and 2. Wait 45 days for iMessage to expire. This is outrageous and not a solution at all.
If you want to see screencaps of my exchange check out my blog post about it: