1. Wrong: Watching Michael Phelps swimming brings joy to millions.
Better: Watching Michael Phelps' swimming brings joy to millions.
Explanation: The object of the gerund watching is the gerund swimming, so Michael Phelpsneeds to become an adjective describing swimming.
2. Wrong: Casey wondered if his husband knew about his plan for them going on a trip to Alaska.
Better: Casey wondered if his husband knew about his plan for their going on a trip to Alaska.
Explanation: The object of the preposition for is the gerund going, which can't be preceded by a noun and must be preceded by a possessive.
3. Wrong: We still had three days drive to get to Graceland.
Better: We still had three days' drive to get to Graceland.
Explanation: The drive will take three days, so the days should be in the possessive case.