is really being neglected? Or does she chooses to place herself out of the way?

Like she chooses to play the piano and not dance, and chose to refuse Charles. Anne seems to have placed herself on a shelf - She seems to have decided that she will always be a third wheel and feels more comfortable when she is out of the way or being useful.

I really think that Anne is playing the part that she has chosen not the Harville or the Musgroves are slighting her.