Sounds like a prime case for powerline plugs to me. Everyone i know who has moved to powerline networking has loved it.
Youd need 2 powerline adaptors, one would go in a plug socket by your parents PC/the router and the other would go with your xbox. The router have an ethernet cable to the downstairs powerline adaptor and your xbox would have an ethernet to the upstairs one. Job done and an end to wireless drops and slow transfer rates.
Cheap option:
http://www.ebuyer.com/product/160665Or more flash and expandable option:
http://www.ebuyer.com/product/154888