Appropriate??

So I am going thru with a divorce. I have been in hope for awhile, thinking that I could somehow 'fix' the unfixable. A light bulb finally went off and I am proceeding with the divorce.
Anyway~ I was unplugging 'his' phone to plug in mine, it lit up and I saw that a certain
women has been texting him. This women has been a problem for awhile, I have had to ask her to stop talking bad about me to MY neighbors, I only called her on it once but word got back to me every time she blabbed info she knew NOTHING about.
I was wondering if this is appropriate? I'm sure my soon to be ex would not have liked me talking and texting other married men, so why is this ok? I guess the bigger question is why can't she wait until he moves out?