When you swing a golf club you should be performing basically the same movement you do when you play virtually any other ball sport: tennis, bowling, volleyball, baseball ... You should be using your body's "core" to hit or throw. Your hands and arms are attached to this powerful "machine" that can propel a tennis ball, baseball (hitting or throwing), bowling ball a surprising distance and at an equally surprising speed when you follow through, shifting that power to the finish of your swing or throw! Hands and arms sort of fine tune your hitting or throwing motion.
Amateur golfers tend to swing and hit the ball with arms and hands, often falling back, rather than using that powerful core. Check out this tip and you'll see what I mean.
Have fun and enjoy the game again.