Many times obeying God does not bring us happiness. Think of Jesus. Jesus did not want to die (Luke 22:42). Do you think Jesus was happy when they were killing him? Of course not! But what does the Bible say? He says that "[...] for the joy set before him he suffered the cross [...]" (Hebrews 12: 2). Jesus was joyful and he was suffering too! Joy is what motivates us to obey God, even when obeying does not make us happy. It would probably bring happiness to your life to kill the neighbor's dog that barks every night at 3am. But obeying the command to love your neighbor goes beyond what would make you happy, for example.
DR