Having been in a relationship where I was not trusted, due to my ExOH insecurities from a previous relationship, and nothing I'd done I would just like to make a couple of points.
It is incredibly stressful, draining and hurtful to continually be checked up on when you KNOW you haven't done anything wrong.
People are saying that if he loves her the OPs DH should be helping her - but noone is superhuman and there does come a point where constantly being accused, checked up on, being called a cheat/liar just gets too much.
It is a horrible situation to be in - and contrary to what people are saying - if he hasn't done anything wrong he must REALLY love her to deal with this.
As I said, I've been in a relationship with a man who was insecure and constantly thought I was cheating. I reassured til I was blue in the face, I showed him my phone, let him read my emails - I did EVERYTHING I possibly could to reassure him and it was never enough. Because the issue wasn't me - he would have been the same no matter who he was with. And one day I had had enough. Had enough of all the accusations, the tears, the phone calls whenever I left the house - even to my work - and when he asked to see my phone I said....
NO. Not because I was hiding anything, but because I had had enough. Showing him my phone/emails whenever he asked previously had NOT CHANGED ANYTHING. It made NO DIFFERENCE - things would be fine for a day or two, and then the questions and accusations would start again.
My point is it is the insecure person who needs to deal with their issue. I agree it's not helpful when the other person refuses, but please please be aware just how hard it is to live in what is effectively a straitjacket. It would take a saint to put up with it indefinitely and not snap at some point. I also think you need to have been there to understand fully what it is like. It is utterly soul destroying, not only because of how it feels to be on the receiving end, but also because you can see the unnecessary pain the person you love is putting themselves through.
In the end I left my ExOH - not for anyone else, but because I simply couldn't take the accusations any more, couldn't take having absolutely no privacy - I never hid anything, never would, but having to hand my phone over every day when I came in, and even then being accused of deleting things just became unbearable. I ended up with depression, I felt guilty because I couldn't make him feel better, I was nervous all the time wondering what would set him off next...
The OP said that her DH had said he couldn't take her phoning him TEN TIMES A NIGHT from work. Couldn't take the accusations and lack of trust. I can totally empathise with him.
But he came back - this time. So he clearly does love the OP very much.
I'm not saying this is all one sided, and I think they would both benefit from some counselling. Because whilst it is hard for the partner of an insecure person it is also incredibly painful being the person who is insecure - constantly on the alert, hyper-vigilant, constantly imagining scenarios etc.
Please OP - go see someone to help with your insecurity - your DH LOVES you, he must because it is so hard to live with someone who doesn't trust you that you couldn't do it without vast amounts of love - but you need to believe it.