He won't let me talk to my kids father...

My boyfriend is a very loving and kind man... But he has trust issues.
My kids father. Lives 19 hours away across the country. Therefore, my kids hardly know thier father. 
We're court order to facetime 3 times a week, which we do successfully.
I do not talk to him directly on facetime, he just talks to the kids.
I can't remember the last time I had a phone call with my ex, the most direct communication that I have with him is through text and only about what time to facetime for that day.
My boyfriend told me he does not want me to talk to my ex.
 I explained that I have to have contact because we share children.
 I want my boyfriend to feel more secure about the situation...So I agreed  that if I needed to talk to him I would let my boyfriend know and I would not speak to the ex unless it was absolutely necessary.
(Sorry this might be long) 
Last night, my ex randomly texted me a photo of a table. Earlier that night he was telling the kids on skype about a table he was making.
I told my boyfriend, I have a text from Chris, I just wanted to let you know. I don't know what it is and we can look at it together.
So we did.
Which lead to reading all the other texts between us. 
The day before he sent a text after we lost connection on a FaceTime, said "give the kids kisses for me, I love you guys"  
I just responded "will do" 
My boyfriend was upset about this.
Then, there was a message were he asked my opinion on his recent break up.
I responded that its between her and him and that Im not comfortable talking to him about it.
I had actually told my boyfriend about this message two weeks ago when it happened. At the time he was like ok, whatever.
Now he sees it again and says why did you respond? You should have ignored it. 
Which I guess he's right. 
At that time I felt proud, like I was doing the right thing by saying what I said.
NOW he starts going through my snaps and deleted photos!!!
Which was so hurtful. I feel like I'm trying to make every effort to show him that he can trust me and he starts doing that.
I have nothing to hide, go and look but the fact that he did, hurt my feelings and made me feel low.
THEN, I wake up in the middle of the night to him snooping on my phone behind my back.
Today he's giving me the cold shoulder like I did something wrong.
I don't know how long I can take this, being treated like a sneak or unfaithful. 
What do I do????? 
It's like, I do what he says and then I still get in trouble.