Why should the real off-spring, the letter writer, have to give up his/her bed for a guest for more than 3-4 days.  I think Dave is out to lunch on this one.
Good for LW to raise the issue.  The cousin needs to go.  To find a life to take
care of, not remain like a spoiled brat.  As to the LW, he/she has inherited rights to stay put until mom throws him/her out, or he/she leaves on own
accord.  Mom needs to put her foot down, with help of LW, who may be only
14-15 and who really should be at home.  Many of us have cousins like this
and what's going on is not right.  Spare me the wisdom of sibling competition.
Sisters know how to speak the truth.