"As a sahp, I don't want to be paid for looking after my own children."
As a SAHP you are being paid for looking after your own children.
You aren't supporting yourself financially - either your husband or public funds (or both) are paying your way so you can look after them.
Also - they are your children, so looking after them is *your responsibility.
Asking someone else to take on your responsibility and recusing to pay them is exploitative.
Saying that if they love the children it wouldn't feel like work is disingenuous bollocks.
I love my children but if I have to look after them all day on my own I don't consider that "fun stuff" and when my mother does it for me (as a favour, because she is kind) I am grateful and know that it is tiring and hard work for her despite how much she enjoys it.
"karma you are spot on, I do want my daughter to myself at the weekends!"
Oh right, so the "unfettered access" to their granddaughter really just means they have to be your unpaid skivvies or fuck off?
Why live so close to them if you don't want to see them at weekends?
"callme I think it's a negotiation and you can meet people half way. Someone does have to be willing to bend and make room in this situation to facilitate things."
Yes, you! You are the one asking for something - you have to be gracious and accommodating and accept it if the answer is no.
There is no negotiation when you are asking someone to do you a favour.
The only "negotiating" you can do here is emotional blackmail - threatening your own daughter's relationship with her grandmother so you can get free childcare.
What a wonderful mother you sound 
"Sometimes you do have to drop all for family because it's a good thing to do."
O M G
Is there no end to your sense of adolescent entitlement?
I would expect that kind of logic from a spoilt 16 year old.
You think other people should "drop everything" to sort out your childcare?
Grow the fuck up, seriously.
Jesus, your poor parents having you as their only nearby child.
I'm sure you'll find a way to charge them every penny for any tiny consideration you do them.