The answer to this is indeed quite simple.
Park wherever you want to (and are able to) whenever you like whilst ensuring you do not contravene any parking restrictions, park on the pavement (even with two wheels) or block anybody's drive.
You have been most co-operative with the van driver and the lady across the road. However, they have no more right to a reserved parking space than you do.
Mediation will not work. The van driver wants the space for his van every day - he will not settle for odd-numbered days or months with an 'R' in them. The lady opposite does not want you to park outside her house at any time (for reasons best known to her, but presumably in case she has a friend drop in for tea) and there is no room for negotiation there either.
You will not avoid upsetting your neighbours but they, of course, had no qualms about upsetting you. It is they, however, who seem to be labouring under the misapprehension that the space outside their house is �theirs� to use or control. They will have to learn, as has been pointed out, that it is "first come, first served" and will have to be prepared for a little disappointment from time to time.
Life�s a bit like that sometimes.