Somebody who is kind, yet hard, but fair

I would call her firm. That implies strictness with kindness, to me.

The freedictionary defines “an iron fist/hand in a velvet glove” as something that you say when you are describing someone who seems to be gentle but is in fact severe and firm.

Maybe you want someone who practices tough love.

I would call her "objectively insightful."

A person who can be considered firm but fair may be tactful

potato means potato so that means another word for firm but kind may be strict, caring or perhaps wanting you to get far in life