Is it too much to ask...

If your man was still friends with his ex but it made you massively uncomfortable, is it too much to ask for him to jack that in? In the past I've had issues because I've seem messages between them where there are sexual innuendo's and private jokes. I don't find it appropriate. Not to mention that I've had issues with him meeting her for lunch and a game of pool a few times but he's done it behind my back after I said I'd rather he didn't go. Now she still messages him and he tells her whats going on in our lives like new house, holidays, engagement etc. I hate that she knows things about our lives. I mean I'm his future and shes his past. I have actually messaged her through Facebook asking her to stop with the flirting and sexual innuendo's because I find it inappropriate but she continues. And he gets all arsey because 'shes a mate'. Is it too much for me to ask him to shut her out of his life because it makes me uncomfortable?