Usually tender is used to describe women, while gentle is used to describe men. So we prefer saying Mom is tender instead of gentle.
Is that right?
No, I can't agree with that at all.
Tender might be more often used to describe someone's disposition and gentle might be used to describe how something was done: a tender disposition, a gentle touch.
They don't have genders associated with them.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.