I've never heard anything like this before, you can't help a child's behaviour by turning your'e back on it. If this CM can't cope then she needs to come clean and say so rather than mucking you and DD about like this.
You say you admit your daughter is spoilt, to me a spoilt child has major stropps, screaming tantrums, feet stamping, throwing, hitting etc, not forgeting to say please/thankyou. If your DD does have any of the above then you need to address the situation otherwise you will probably have similar issues with other childcare providers, however from what you say your DD sounds like a pretty normal 3yo to me.
I'm surprised that if your DD has been with this cm for three years that she doesn't know the house rules yet, usually only takes a couple of weeks at most, sounds like theres a bit more to things I would ask your CM what the real issue is and tell her to decide what she wants to do so you can make arrangements if needed.
And as for the painting thing I'm sorry but I'm a cm and I would have told her to get over herself, kids live for mess, mine get covered from head to foot in clay, paint, glue, sand water and sometimes stuff that I'm not even sure what it is, has your DD never done any messy play in the 3 yrs she's been with her?
Think I agree with the others find someone else or a nursery with sensible staff.