Find another CM!
I have been in Childcare for 30 years, and in that time I have had some, shall we say 'challanging children', I would never do as your CM has! Totally shocked!
3 year olds, no matter whether they are spoilt or not, are stubborn little monkeys, it goes with the age.
Your CM should have a Behaviour Mangement Policy, have you seen it, has she talk through with you, the way she is managing your DD, do you have a diary to see what is happening each day?
You do seem to realise that your DD's behaviour can be a bit difficult at times, and are adressing it, but you say she is not as difficult with you as with the CM, is she with other people?
Is she bored at CM's?
Would a Nursery be better at her age, would be more sociable, and you would get Nursery vouchers at her age.