I don't think an "ordinary" nursery would be more flexible than a childminder (perish the thought!!) Would imagine that they would charge full-fee all week, even if you cancelled a day, and wouldn't be too happy if you were late. I'm sure there's a recent thread about nurseries near airports possibly offering weekend care, so I guess they might be more flexible?? Other airline/airport staff must need childcare, don't know what they do??
I know of one minder who took on this type of work for two children, and have to say that it was very difficult for her (but she desperately needed to fill her places). The parents only wanted her roughly every other month, but they were charged a set amount each month for a minimum number of hours (and had to pay more if it was more hours, obviously).
One month would therefore be quite easy with little or no minding work (but no way for minder to take on anyone else unless it was an "occasional" booking). The other month involved a combination of very early morning starts/very late night finishes/overnight/weekends and no guarantee that she would finish at the agreed time anyway (long haul flights so possibility of delays).
Whilst I don't want to be negative (but I'm going to be - sorry), it was a job that no other minder in the area wanted. It completely trashed this minder's homelife during her working month, with no end of last-minute schedule changes, and no idea when a parent might return. The amount of money paid wasn't enough to cushion the fallout with her own family (she had a toddler of her own too).
Many minders don't work weekends - would this be when your nan would help out?