Looking after Grandchild ?

I think the first ground rule is to make sure your childminding services are wanted.
It doesn't sound as if it has been clearly spoken about yet, so that needs to be the first step.

Don’t fall into the trap of thinking you have to take your GD out all the time. I looked after three GC, one after the other, and we used to entertain them at home. We had a good supply of toys and books (charity shops and car boots) and we did lots of painting / crafts with them as well as cooking. We took them out if we needed to go out shopping or sometimes for a walk. We did take them to classes such as Monkey Music if the parents had booked them. We have a wonderful relationship with all three GC who now ask to visit us, often to paint or cook. However, we always followed the parents’ rules to the letter no matter how tiresome these were.

I would say it's a joy and a privilege and just go with the flow. I tried to be organised in terms of food prepared for the day and little activities for the child. Ask for a bag to be brought with all her bits and pieces and gradually keep spares at your house.
It will evolve as you go along, so just enjoy the precious time because they grow up so fast.

If you are allowed to do this then you must ensure you stick to the parents rules or trouble will follow. Parenting has changed since our day.
I would also think long and hard about how much just one day a week would tie you down, never being able to go away for a week etc.
Personally I would prefer being the emergency childcare and babysitter to allow them some time alone together. You would be more appreciated.

Be prepared that your daughter may decline your offer. Don't get too excited or decide it will happen, or you are setting yourself up for disappointment. You sound like you've already made a lot of decisions on the assumption this will happen. Your GC's parents may not want GP care or may prefer what they perceive as the benefits of a care centre.

As far as ground rules - my ground rules would be that it happens on a day that works for me and that I am allowed to take the child out for walks, to the playground, etc. Otherwise, the parents are the ones that will set most of the rules about how they want their child cared for.