The problem is that cleaning is subjective, what one person deems 'a great help' another deems 'overstepping the mark'.
OP - I don't think it is bad to have private areas of the home where cleaners shouldn't go into without work in that area being booked, we don't allow the cleaning staff to go beyond the areas promised to client within our standard service, however I can understand that some self-employed cleaners (individuals I mean) have not yet learned to set out the scope of their service and what it may include in advance and shown this to the client, they should also discuss any additional areas that the client wants done and will allow them to clean at the point where the cleaner gives her quote. Therefore everyone knows where she will be going and what she will be doing and seeing and there can be no confusion.
We do not allow our cleaners to stray into areas we have not set out within our service UNLESS the client books additional work in advance so that we are all on the same page on this and do not cross any lines, plus the client is always receiving what has been agreed, booked and paid for and there is no misunderstanding or dissatisfaction. These are things you learn with experience and I am there to take care of the structure of the service in this way. This cleaner is an individual who has to find her own way and may not be aware of these subtle personal boundaries yet. She is human and she made a well-intentioned mistake through lack of experience, most people would not mind and would be pleased that she did offer additional services, such as laundry as this is not a usual service offered by cleaners.
You can't 'sack' her as you don't 'employ' her (unless, of course, you run payroll and make the necessary deductions plus keep a record of her holiday entitlements and other statutory rights). If you 'employed' her you would not get away with sacking her for this, she would need a documented verbal warning then for the next 'offence' a written warning, then a final warning (all documented and signed by her) and then you could dismiss her. However, you don't employ her so if you don't like her service, just cancel, if she has a notice period written within her service agreement you may have to have her a couple more times but otherwise you can change service providers immediately.
That is where you stand legally but I don't think this relationship will last much longer either way, cleaners tend to sense when someone is not happy with their best and unless they work for a company and their boss wishes to keep on the client they will tend to swap out the client for someone new.