As long as she fights transparency and claims you are snooping or spying on her, she's not ready. If she has nothing to hide, she should not have any problem with her H having access to her messages. To me, it's that simple, and until you have her 100% cooperation in the transparency.....she has another person in the M.
When a person is transparent, you aren't spying, right?
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!