Taking a kid to places 1 day a week may or not be "helping with the child's development" - that is a very dangerous and loaded statement\
*If the child is going to a playdate - sure
If it is grandma or grandpa running their errands - not at all*
Hmmmm.... I think "running errands" CAN be a big part of a child's development...and an advantage for grandparents is that they may well have more time than their parents.
- Going shopping, talking about the purchases, finding things on the shelves, picking out the different fruit and vegetables, discussing the larger and smaller items, looking at the numbers for the prices, putting them in the trolley, helping at the checkout, as they get older maybe touching the card on the machine, ......lots of learning in there and lots of conversation.
Maybe it is walking somewhere together - discussing the colours of cars, flowers, trees, etc, maybe finding numbers on the cars, or door numbers. Seeing an aeroplane , wondering where it is going, talking about that place. Maybe seeing a bird, or a worm or whatever! Maybe seeing rubbish on the pavement, talking bout that and what should be done with litter. Crossing the road, pressing the light and waiting.
Then there is the potential for "helping" to make a meal - washing vegetables, laying a table, counting how many people and places, getting out cutlery, when older chopping vegs, or serving up, or carrying plates ...stirring and watching how things mix together, using a whisk, learning to crack an egg...and so on!!
Or helping with cleaning - dusting, using the dustpan, tidying books/papers etc ....
All of these "Errands" and jobs include lots of potential learning development with an adult who uses the time and has the time... whether that is a parent, a grandparent or some other trusted adult!