Sounds about right, driver is a challenging club to hit and im sure your not the only one that can hit their 3 wood just as far if no further then there driver. I see it all the time. I was in the same boat for a while, what i came to realize was that i was holding back and making a 3/4 arm swing before w the big dog because i was worried about spraying the ball, but after i got fitted for a shaft that required me to go after it, the distance come and my swing has started to solidify. I still spray it, but its 25 yards further still then the 3 wood.
A 3 wood is easier to hit with a poor swing because your hitting down on the ball with wood's, and its hard to hit down on a ball that is tee'd up 3 inches, like the driver. Most people compensate, use their arms to control the club face, and swing over the top with the driver and only deliver a glancing blow, thus in the proccess, loosing distance due to poor smash factor. Your driver isnt a dud, and your situation isn't hopeless. Maybe you can start by teeing the ball lower to see if that allows you to feel the clubs at the bottom of the swing arc. Just look at Bubba he tees the ball like a mile high and swings up on it, where as Sergio tees the ball just barely and makes a decending blow on the ball.
Good luck!