What happens if the Cardinals get stuck with a Pope they don't like? Do they still have to obey him?
Life goes on as usual for all the cardinal of the Church after the election of a new Pope. They must obey the new Sovereign Pontiff in filial joy and reverence. Nor do any of the cardinals have to worry about any chance of a reprisal if some had indeed voted for another candidate. In the Apostolic Constitution Universi dominici Gregis of Pope John Paul II (1996) which deals with all aspects of a papal election, it requires that all the cardinals try to camouflage their writing on their ballots, so as to protect the identity of which cardinal votes for who. Even the new Pope does not know who actually voted for him. After the election of a pope, secrecy must be maintained as to what has transpired during the conclave.
Yes. As the Pope is head of the Church, and designated successor to Peter, the first Pope, who Catholics understand to have been appointed the head of the church, Cardinals are obligated to obey the Pope in some matters related to the church, especially relating to faith and morals, just as any other member of the Catholic Church is. In other areas, for example which football team to support, they are not obey obliged to the Pope.