That would be news to King William IV. He clashed repeatedly either his Sister-in-Law the Duchess of Kent over how the future Queen Victoria was being raised. He publicly criticized her but never prevented the Duchess from raising her daughter. (Preventing the Duchess from becoming Regent was another matter entirely.)
I think you are looking at theory rather than reality. The Queen might have a reserve power lurking somewhere but there is no way on God’s green Earth that she would or could take custody of her great grandson from his parents, even if the boy wasn’t in Canada.
King William IV and the actress Mrs. Jordan? 5 boys/5 girls, she got just the girls back until she broke the agreement to stay off the stage. And back to court they were brought, to rejoin their brothers.
I'm not sure that the Preogative would apply to Victoria in the 4th's case, tho, because Victoria, his eventual successor, was his brother's issue, but not his direct line.
I see where he would be upset with the Duchess tho. In his 60’s with no legitimate children, no luck on producing heirs with his new young wife Adelaide, his brothers dead, so that by 1830 there was a succession crisis, and Victoria, at one time 6th or so in line became both heir and spare presumptive, to be called to court to assume some duties (sliding back to spare if Adelaide had surviving children). I can also see where the Duchess of Kent, a little wackadoodle herself with laundry of her own, wouldn't want her daughter exposed to the 10 illegitimate Fitzclarence children, coveting her dead husband's crown over any issue from Adelaine. Kent refused to attend the 4th's coronation and was willing to publish a laundry list of the King's doings, disasterous at a time rival dukes were jostling for claim. So the king declared he would not die until Victoria was 18. Quite a backstory!