Is it a healthy relationship for a mother to tell her child that they are not trying hard enough even when they're doing their best?

No, that will not help the kids self esteem later on.

It's not an healthy relationship between a child and a mother.

A good relation between a child and a mother is where they alway's say "Great Job" or "I'm so proud of you".

Telling a child your not doing enough isn't healthy, which will most likely effect the child's self-esteem.

A mother shouldn't say a child isn't doing hard enough, when a child is doing their best.

That being said, the answer is: It's not a healthy  relationship between a child and a mother.