Timeshare Exchanges
Well, you (and hopefully your mother) have learned the cardinal rule of divesting yourself of ownership. Never, ever pay anyone a large, upfront fee to sell, rent out, market, or "cancel" your timeshare.
That being said, if you just want to give it away, list it here in RedWeek's Bargain Basement. Offer to pay the closing costs. Legaltimesharetransfers.com will do this for about $150.
Also, Timeshare Users Group (aka TUG; tugbbs.com) has a Bargain Deals section under the "Buying, Selling, and Renting" forum where, for free, you can advertise that you want to give your timeshare away. Just follow the instructions at the top of that forum.