Quote: He said 'You're looking very summery today.' (I was wearing a purple long sleeved top and a pink mini skirt).
Jo, don't stammer with explanations for what you're wearing. Just confidently and with quiet, direct eye contact and a smile, say "Thank you!" I think he really wants to make peace and be friends again, but is afraid of your anger toward him. Being at peace already, and friendly, and allowing quiet/space will let you see his next move, hopefully toward you.
Quote: he told me ...that he'll have to download another programme onto my computer next time he visits. I laughed and told him I would have another angry customer as he wants his pdf document NOW.
Maybe just another thank you here, or an acknowledgement about his own busy schedule. You want to highlight your independence and yet your appreciation for his unsolicited help. Then thank him notably when it happens. Again, this will pull him toward you over time.
Quote: I have had this horrible headache all day and he noticed me pressing on my temples, so he said 'I hope your headache goes away soon.'
It was nice of him to notice. Maybe next time, he'll act on that hope and offer to help massage the headache away. If not, maybe your request to do so would be a safe way of initiating PT, when things are friendlier: "Would you mind rubbing my temples/base of neck for a few minutes? I just can't seem to do it like you do."
I like that you didn't ask to go to the ballet. Your girls are so wise - they gave Mommy and Daddy space to work things out a bit!
My take is that he's trying to make peace. Meet him halfway, with confidence and some subtle offers toward connection that go beyond requests for computer aid, but are more directed right at you and H.
I think he really wants to make peace and be friends again, but is afraid of your anger toward him. Being at peace already, and friendly, and allowing quiet/space will let you see his next move, hopefully toward you. 
