To be honest, I really struggle with this.
It tends to be women work, or work that is done in the home, or work that is done on a part time basis, or work not governed by employment contracts where such attitudes pervade.
Imagine this person is not a child minder but a shopworker...working at a shop through an agency. Should Sainsburys not pay that worker more because they are doing a great job and are valuable to them in case Morrisons can not pay the same?
I do not believe that "just" because someone is a child minder and self employed they are therefore different..because that is what women have been fighting for hundreds of years, equal pay, equal value, equal recognition.
People should be paid their worth. We can not have a situation where a child minder is treated differently specifically because they are a child minder. Your child minder is personally not responsible for the local market rate for child minders.
In any other area of work or service, you pay what it is worth to you, subject to minimum wage legislation.
I do not believe you should keep someone's wages down on purpose, because you fear other employers/people that are paying for a service can not also meet the same rate.