Am I being irrational?

So my fiance continues to text "good morning beautiful" to his ex wife and insists on going over there to cook her dinner several times a month. I have expressed on several occasions that there needs to be boundaries and I am not comfortable with that. His response is always basically well I want to remain friends with her so your gonna have to get over it. This is not an outlandish request right? I am all for being cordial and civil and all that. I even told him speak to her the way you would a coworker, friendly polite, surface level info and he told me he wouldn't call her pet names anymore if I wasn't comfortable with it. Well I went through his phone (before you judge me I know I already feel like shit about it) and just 3 days ago he text her "hey I haven't said good morning to you in a while so I wanted to say good morning beautiful" I am so upset once again. I feel like I am beating a dead horse. I am also terrified to bring it up because obviously I crossed a line going through his phone. Is this a normal relationship and I am just overreacting?