Question

no sooner did the child see his mother, he rushed to her. (use hardly.... when )

Answer 1

Hey there! ☺☻☺

No sooner did the child see his mother, he rushed to her. 

Rules to change: 
We apply had after hardly.
We apply when at the place of than.
Apply verb third form in first part of sentence.

Answer:
Hardly had the child seen his mother when he rushed to her.

Hope It Helps You! ☺☻☺

Answer 2

Hi,

Here is your answer,

Hardly had the child seen his mother when he rushed to her.

Hope it helps you!