Reggi,

One thing about close relationships it brings up our “stuff” which we need to work on.  In a way, this has nothing to do with his ex but more about your insecurities and anxiety.  This highlights what you need to work on for yourself.

Have you done anything with your anxiety?  Therapy? Medication? Meditation? Exercise? Mindfulness?

In addition, you can take your bf aside and ask him to ask his parents not to talk about his ex so much in your presence.  Since you have been with him for almost two years then I assume you can be vulnerable and honest with him about your insecurities.

Mark