Hey Suzanne, it sounds a pretty difficult situation, but one you can get over. I've just met somebody who is lovely, but sounds like she was treated pretty badly by an ex bloke.
The other night she heard my phone beep and (a text from my mum, remindig me of my neice's birthday!) but made the mistake of checking the message over my shoulder. I clocked her doing it and she was mortified...I wasn't bothered at all as I have nothing to hide, but she had a cathartic moment of "when you've been with someone you can't trust it makes you suspicious".
What I would say, as someone who has lived a varied life and considers himself wordly wise is that an hour on the phone to an ex partner is somewhat odd, if you are not party to the conversation. Lots of people have to get on with ex partners for various reasons, I do with mine, but an hour to me smacks of more than sorting domestic arrangements!
I think you probably know the answer for yourslef and are jsut seeking some reassurance of your own feelings, which is completely understandable. My own advice..look after number 1. Hope that helps.