I understand that the childminder can take on or not take on any child she wants without even giving a reason, but in this case DN has already been attending for several years so the childminder is actively refusing to care for her anymore. Does this make a difference?
If it was just that she was fed up, I'd agree (though so far as I know, she has the right legally.). However, I think that what makes a difference is Covid. Add strict hygiene rules and fear of infection to the general difficulty of cleaning up after a child this age, and I can understand why the childminder might be worried.
In any case, I think the big problem to sort out first is not so much the childminder as whether the child, even with no SEN in the strict sense, may have physical or mental health problems causing this soiling. If she does, then the sooner they are diagnosed, the easier they will be to sort out. Also, if the problem continues as she gets older, especially without a known cause, other children may avoid her, or may even bully her, which would in itself add to the difficulties.
I doubt that the problem is just due to inefficient toilet training.