I'm going to invalidate my sister's feelings
I hope you're kidding. Why would you want to invalidate her feelings?
Because I think she's being irrational.
That may be a valid reason, but it still doesn't justify what you're doing to her.  You shouldn't just reject the feelings of your family members, regardless of the reason you feel you should.  It's not what family members are supposed to do to each other!
My sister should learn to be mature and not act like a 5-year-old.
Telling her that her feelings are invalid isn't going to stop her from acting childish. I think it would be better if you recognized why she's feeling that way, and helped her to see things in a more mature way.