I remember that episode. If I remember she was mostly running to have a female option. She didn’t have any plans or ambition, just the council needed someone with a vagina on it. And like you said Howard had ideas and ambition.
Aunt Bea ends up endorsing Howard I believe after she looks foolish in a debate. I've watched too much Andy Griffith, lol.
They pulled a lot of soft Bea feminist shit especially after the show switched to color.
Howard wasn't acting like a child. He's part of the Church Finance committee and suggests a prudent suggestion for the money. When he sees how important the robes are to Bea, he looks for a solution to help Bea and the foundation problem. I don't see what Howard did wrong or how he was being childish or emotional.
I wonder what she meant by "Hot Wheels", if not the obvious? It's not even a disparaging name.