The long story is:
I returned to work after adoption leave and asked for a reduction in my work hours (from 4 days per week to 3 days per week worked over 4 days) which was refused. I really don't like commuting so I applied for a job which is walking distance from home.
After two very long interviews I was offered the job, but 4 days a week (not 3 as I wanted).
I accepted the job by email, but when I told my current employer my director asked what he could do to make me stay with them. They have now come up with a package that suits me very well (3 days per week, 2 full and 2 half days, worked mostly from home so I only have to commute once or twice a week). I'm annoyed that they didn't do this when I first asked for it, but not annoyed enough to leave anyway out of spite.
I haven't signed the contracts with the new job and now I have to tell them that I'm not accepting the job. I do genuinely feel bad about it, they are very busy and really need an extra person and the time spent interviewing me has been wasted as it also means that they have to start again from scratch.
I tried to phone so that I could explain in person, but neither of people who interviewed me were available. I'm really bad a putting this kind of thing into writing. Advice please, should I tell them the whole story, or just keep it simple and tell them I've decided to stay with my current company?