How much would you

Maybe half their hourly rate per journey per child? So a full hourly rate per pick up or drop off?

If you're asking childminders, they will almost certainly have a set rate. They may not all be the same.

Childminders cannot be used as a taxi service as it affects their insurance. You will probably have to pay a set rate for min 2 hours per morn/afternoon.

As a childminder I would charge you my standard rates: £7.50 before school, £15 after or £21 for both (& that's assuming I already did that school run). I can't imagine many childminders wanting to give up 2 spaces in their car for less than full morning or after school fees I'm afraid.

If it's someone doing it as a favour but not already doing the school run i.e. Using their time & fuel, I'd say £10 each drop or collect so £20a day.

If however it's a mum already doing that school run with car space, an extra £10 a day cash would come in very handy !

A taxi company charged £10/drop off or collection for such service two years ago.
A childminder (if you're lucky enough to find one that would be happy to do it) will most probably have a set fee per child for afterschool care even though you'd only use 15 minutes of it. They would take spaces in her car therefore making them unavailable for other children who'd like to use her for a longer amount of time. This could be an equivalent of 2 or 3 hours of care per child.