If the beneficiaries of the trust do not want the timeshare, then the successor trustee can sell or otherwise dispose of the asset. I’m not using the term “asset” to connote value (ie asset vs liability), rather it’s an asset that is owned by the trust and carries a title, such that it requires that title to be conveyed legally to who ever will be the owner. As to who manages it, initially it would be th grantor of the trust, then it would shift to the successor trustee if and when the grantor resigns, becomes incapacitated or dies.