You're Correct!
If you find that all your approach shots are missing short right of the green, then all that is happening is your club face is aiming right of target, or it is open at impact, if you are a right handed golfer.
To correct this, all you have to do is aim the club face at the target as you are striking. If your golf club face is open as you are hitting, you are putting more loft on to the golf club face, so that the face angle, or loft, has increased on the golf club and the result of this is that you are going to hit a much higher shot than normal. As a result of this higher shot, the ball will now land short of the green because it is travelling into the air more than it is going forward.
If your club face is open, it is also aiming right of the target as you strike the ball. If the club face is aiming right of the target as you strike the golf ball, the golf ball will now fly right of target as well. Hence you get a short, right shot because of the open club face.
In order to correct this issue and to get you hitting straighter shots that make the green, you need to ensure that your club face is square to the target, or aiming at the target, as you strike the ball. Initially, you need to ensure that you have the club face aiming correctly at the target in your address position. If you place an alignment pole on the ground to represent the target line, you want to now place the club head at the right end of this pole and ensure that the club face makes a right angle to the pole/target line.
Check that your hands are on the club correctly, because if they are not, this could be the reason that your club face is open at impact. To check this, first of all look at your left hand, if you are a right handed golfer. Take a coin and place it between your left thumb and your left hand. You want to make sure that when you are holding the coin between your left thumb and your hand, the coin is centred on the top of the handle and that the coin is pointing to your right shoulder. If that is correct, your hand is in the correct position if the coin is pointing at your right shoulder. If you place a coin between your right thumb and hand, the coin being held in this hand should also point to your right shoulder.
If you are holding the golf club, so that you can hold a coin and it points at your right shoulder, then your hands are on the club correctly and in a position that will promote you to return the club face back to the golf ball, with the club face square, or aiming at the target.
Make sure you swing and maintain the club face aiming at the target through impact. Here is a great drill to help you with that. The next time you go down to the driving range, or the practise ground, just take a length of rope with you, maybe five to ten metres, or if you do not have any rope available just take an alignment pole, or an additional golf club. Before you hit your shot put the rope out in front of the ball, about a metre in front of the ball on the target line, to show you the line that goes from the ball to the target, allowing you to actually visually see it.
Make some slow soft swings to start with and then introduce the golf ball making the same slow, soft swing. Work on hitting the golf ball directly along the line. If your club face is open the ball will be going to the right of the line. Work on turning the club face a little bit more to the left so that you start to hit the ball out directly along that line.
As you start to feel more confident with this, you can swing the club a little bit quicker and start to make a bigger back swing so that you begin to swing more towards the speed that you actually swing at, out on the golf course. Initially, do this slowly and softly to get used to the feeling to start with, that gets the ball moving directly along the rope/target line and work on hitting the ball directly along the line and as close to it as possible. That will really help you get your club face square at impact, meaning that the club face is aiming down the target line and at the target at impact. This will start to get you hitting shots much further and at the target rather than short and right.
Sorry Try Again! - See Explanation Below
This type of strong grip would normally close the club face and produce long and left shots.
Sorry Try Again! - See Explanation Below
This type of hand action would often produce high, short but to the left of the green golf shots.
Sorry Try Again! - See Explanation Below
If you were aiming right of the green, the ball would miss the target on the right. However, the length of the shot would be the required length. Aiming right of target does not produce shots that miss right and short. They miss right but are of the correct length. The club face being open through impact produces short, right golf shots.