I'm getting the feeling that Annie does not know how to respond to Joan.
Annie relies--when you get right down to it--on intimidation--especially of women.
She can't intimidate Joan--so she just kind of clams up when Joan goes after her.
IMO Annie is not as "strong" as she wants us to believe--her touting her "strength" constantly is all part of her self-created persona.
And where Annie talks strength-Joan actually IS strong to have survived and thrived for so many years.
My money's on Joan.