Can you give a rough estimate on this repair?

Sounds like they left the motor mounts , or transmission mounts loose, In regards to your transmission all automatic transmissions are hydraulic . they carry around 10 to 20 quarts of fluid the fluid is used to apply bands and servos for changes in speeds the torque converter act as a fluid coupling between motor and transmission . Transmission fluid and filter change should be done before 100k miles and cost around $100 if they back-flush the torque converter.