There's no concern about payment agnesnitt, but it's like anything...if you ask a mate to do you a favour and she doesn't do it quite the way you'd hope, you have no come back. If you pay someone to do something for you, you have more of a right to impose sanctions, dictate rules, etc.
In the case of childcare, you talk as if the grandmother in this case has no rights. Like someone said earlier, the child wasn't left on a bench or neglected. And we don't know whether the gm understood the request from the op.
In this case, I say that the op has choices. She trusts her mum to take her child and care for her, or she doesn't. If mum explains to GM that she really wasn't happy about the creche situation, it may be the gm didn't realise how serious she was. Parent/child relationships are full of assumptions and misunderstandings.
Personally, I might be unhappy at daughter being left in a creche, but I'd make sure my mum was made aware of this and I'd give her the benefit of the doubt.
From the numerous posts from the OP it sounds like the relationship between these two adults isn't great. In my shoes, faced with a lack of trust in mum, I wouldn't trust her with my 3 year old...full stop.
As the OP she has, she has to live with the fact that her mum is an adult...she's not the childs parent, but whilst she's caring for the child, she has the right to do whatever she wants, as long as the child is safe.
End of....