Would can be used to describe something imaginary, but here "wouldn't" is the past tense of "won't", and describes her intentions.
She wouldn't look at me in the meeting = she refused to look at me in the meeting.
She didn't look at me in the meeting = only describes her actions, without telling us why something happened e.g perhaps she was thinking about something else, or looking out the window, or didn't know you were there.
However, because of the first sentence about making eye-contact, we can assume that she deliberately didn't look at you during the meeting because she was following a social convention.
Although "decided not to do something because of a rule", and "refused to do something" aren't 100% the same, in this case the meaning of the two sentences is essentially the same.