It's not cheating, per se. After all, as you concede, she needs to be able to communicate with him in order to do her job.
Personally, I would intensely dislike being told who I can communicate with, or how often.
But going beyond that--- it's hurtful in that you've repeatedly asked her to stop yet she persists. And it's problematic in that she's lied about changing her behavior.
You need to decide whether it's a dealbreaker.