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.
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.