B - thanks for the response. He still cares and yes he still thinks about me. It comes to naught though. He has not said or done anything that indicates he wants to R. Picking some trainers for me (or sorting out my tires - which he also did today) does not a reconciliation make.
You are also right re the conflict avoidance. He will not respond. He has dropped the girls off, we talked for about half an hour (mostly about D9's glasses) and now he has gone to take our dog for a walk. There was an uncomfortable moment when I said I am getting his brokers exGF to watch the children Thursday night and he said "I don't agree with that - can't you sort our nights out for the nights I have the girls". I told him not everyone's life revolves around his schedule.
A couple of months after BD, he went to China for a week for an interview. I only found out because I saw the website on my laptop (I looked at the history). When I confronted him he said he was "exploring options". He was so unhappy and desperate to escape his life, he was willing to explore work options on the other side of the world. He never told me how it went or indeed anything at all about his trip. As he is not working in China, I assume he decided that a contract which meant that he would be away from the children for four weeks at a time was probably not something he wanted to pursue. A quick google search told me that this was all that was on offer. He went there for a week to find out the same thing. Anyway. whilst he was away I wrote him a lengthy email saying how I felt, how much I still loved him, and how I was willing to let him go if that was what he wanted but that the door would still be open. I included some intimate details in there as well - nothing graphic, but it was mentioned in the sense of how I felt. I sent it to his sister (we were still talking then) because I needed someone to tell me if it was too much. She said, well, it tells him how you feel, so I sent it. He has never responded or mentioned it other than to tell me that he was upset that I had showed it to his sister. I bared my soul and all he could say was "don't send stuff like that to my sister". So, if he couldn't respond to that, I doubt he will respond to an email talking about logistical practicalities.