::Cracks knuckles::
First off define, "get way on my right side." Where do you feel the weight at the top of your swing? It should never get on the outer portion of the trail foot. If that's the case, you need to feel more 'centered' on the ball. While axis tilt is desirable trait, too much might prevent you from making a solid pivot.
From down the line what do you see? Most people who have an out to in swing have to swing around their right hip. It's in the way and a steep path is necessary to hit the ball.
Also, from down the line make sure the right forearm is under the left. Get those wedges set. That makes finding the inside a LOT easier.
Now onto fixing the path. IMO, the vast majority of path problems come from the idea that you are hunting the ball. Instead of making a swing, you are trying to beat the ball as hard as you can. Any jerky motion from the top of the swing is enough to pull you off plane and make you steep. Things like plane lasers or flashlights will help get the feel of staying on plane. You can also build your own inside approach, or simply place a head cover next to the ball. These things will get you to hit the ball from the inside.
In one of Brian's articles, (perfect pivot or something) he talks about making a big enough shoulder turn so you are able to get the right shoulder back deep enough so it can get on the right track. That's been huge for me over the years. When I get lazy, my arms travel up and across my chest, but the shoulders are not getting to where they need to me.
You can also try to fix your club face first. Are you pulling shots to the left? Or do you slice? If you slice, fix the face so you are pulling them to the left. Now your computer (brain) will recognize that in order to make the ball go straight, or start right, it needs place the club on a different path.
Wally Armstrong has a terrific drill that I absolutely love regarding path and what the shoulders need to do.
Grab a frisbee, or plastic dinner plate (nothing that your wife would get pissed at if you drop it). Hold the plate in front of you with your left hand at the 9 o'clock position and the right hand at the 3 o'clock position; sort of like if you are driving your car.
Now. Pretend you are addressing the ball. The plate is still out in front of you, sort of over your target line. Go ahead and make a turn back behind the ball (keeping the points I mentioned earlier in mind). All we did is turn, the arms didn't move or down, they are still parallel with the ground. Your right shoulder is behind the ball, and NOW I want you to ROTATE the plate CLOCKWISE 90 degrees. NOW turn back to the ball. Do this move 54436342364342343 times. Do you feel the dropping action of the right shoulder?
Make the turn.
While still turned, ROTATE THE PLATE.
Turn back to the ball.
Repeat.
Notice that there was no jerky motion to the ball. There was no premature rotation of the hips or shoulders. Rather things moved DOWN first INSTEAD of out. You see it's a SEQUENCING problem.
Good luck.