Alright so there are two basic things that I do with my daughter to allow her left handed swing to become more natural.
1 - Train each hand independently.
2 - Make sure the top arm elbow slots correctly.
#2 is not something I concentrate on with someone hitting from their natural slide because if you do some other things right, that usually takes care of itself. And I've actually found that if you focus on it too much on the natural side there tends to be a dip in the swing and you come out of the proper swing plane.
1 - Train each hand independently.
The bottom hand (her right hand) is the FOR HER. If she gets that well oiled the top hand is not as much of a problem. We use a small bat like a t-ball bat, one that she can handle without having to focus on it.
We take slow swings through the phases I have set up for her, stopping at each point to check things out. We do that a few times. Stance, load, launch, contact and follow-thru are the names we have given them. In the off-season we go through them about 5-8 times and then each time we go hit we do it again and she gets better at it. All one arm at a time.
We then get on the tee and step though the 5 phases again a few times to get lined up. We then take some slow, smooth swings to allow her to feel that she can generate power with slow strokes and doesn't need to get all out of whack trying to hit the ball hard. Each time she does a few smoothly we rotate a bit harder. We keep doing that until she is on the edge of control. And if we keep doing that what was on the edge of control will now just be her "hard swing" and she will have a NEW edge of control. Repeat for the top hand.
We move on to soft toss from the front using smooth strokes then hard. Her hard strokes are her "no strikes" swing and her smooth strokes are the normal swings she takes in a game with one strike on her.
Those two things are the staples of my one armed training. Occasionally we will do some other things if I am trouble-shooting her swing but that is as needed.
Next post.... arm/elbow slot