Did your mother offer or did you ask? Does your mother need the money?
I think it's a strange situation but you and your mother seem a bit weird about this.
You begrudge paying your Mum for the childcare, thinking that she should want to look after your child. Why would you think it was free of charge?
Your Mum didn't mention the payment to you, was she waiting for you to offer?
If you could have arranged another childminder... why didn't you?
If you report your Mum to the tax office though, you would be really unreasonable.
To be honest, if my Mum would look after my child, I'd happily pay the childminder charge for the week. If she offered to do it for free, I would have maybe taken her to a spa or something nice in return.
You have a strange relationship with your Mum... and she with you. 