Complex sentence: Meg shares that she cut Lisa's name into her arm so that she will always remember her, much to Lisa's disgust, who gives Meg her saxophone, which Peter throws away since they do not have room for any more luggage.
Split into simpler sentences: Meg shares that she cut Lisa's name into her arm so that she will always remember her, much to Lisa's disgust. Lisa gives Meg her saxophone, but Peter throws it away, claiming that they do not have room for any more luggage.