Various things at play.
But yes anyone working in a school can use reasonable force under the law.
I would put in writing to the school the following because what they are doing and saying is contradictory.
Dear HT/teacher
Thankyou for your discussion on x date at x time where you informed me you needed to grab x by the x because he was doing x.
I understand using reasonable force is within the dfe guidance for use of reasonable force in schools.
However, what I don't understand is the conflicting information you have given. You are fully aware that I am finding it extremely difficult to get x and x to listen at home and both me and childminder feel it's outsized the normal development.
You have communicated to me that you don't agree with this and their behaviour is within the normal boundary's.
Therefore my question is - if x behaviour is within normal boundaries why was it necessary to use the final resort of physical intervention to support his behaviour?
Please respond within 5 working days in writing.
Regards
Don't add anything more. Let them come to you. You aren't accusing them of doing anything wrong and it's likely teacher wasn't as she was very open with you. But what you will have is written evidence to support you.