Can my ex read my iMessages?

Scenario: I have an iPhone 5 and MacBook Pro. I use iMessages a lot while working. My estranged wife (who lives in another country) has an iPhone and just received an iPad from her aunt.

Problem: We use the same Apple ID username and password. That way, the music library is shared and the apps for my son that was bought using my username could be accessed. I do not want to stop giving her access to the user and pw.

Question: If she has iMessage on that new iPad, can she read the messages i text with my iPhone that I send back and forth between my friends. There are some things I text my friends about my strained relationship with my wife that I would not prefer her to read.

Here is a link how to sync them, it has useful info on how to know if that's what she did and how to change it. It also depends how she sat up the iPad.

As long as you do not have a wife. Otherwise you might make your wife jealous.