Welcome to the site and it is a great place to come and learn. There are some wonderful posters who are coaches, parents who have / had sons that been there and done that and various other people. Overall it is a place with very little fighting - especially when beliefs and philosophies are challenged.
As for your question here is my take.
Purpose of hitting the ball deep in the zone is to recognize the type of pitch it is and location. The deeper you can let a pitch get into the zone the better chance you have of making adjustments. Also, don't think that letting the ball get deep into the zone means that you always hit to the opposite field. What you need to do is develop bat speed to allow an inside pitch to get deep but still be quick enough to turn on it. Most drills are designed to hit the ball the other way but it can translate over to inside pitches as well.
One thing to remember in the swing is, as floridafan said, to have the weight stay back which allows your hands to stay back so you can let the ball get deeper into the zone. Your son probably already knows this since he's got good coaches but hitters need to separate the stride and swing into two separate motions. In fact some people teach just a heel lift instead of the stride. To me it's a comfort issue and as long as you can get the foot down on guys who throw heat you will be fine.
A way to recognize if a hitter is keeping their weight back is to know what the back leg is doing. If the back leg is straightening then the weight is shifting forward and totally throwing the swing path out of whack. Use the back leg to help generate bat speed and power by opening the hips up but the back leg will never straighten out.
Drills that help
What floridafan mentioned about using the outside part of the plate it is a great idea but I would use it after doing several drills.
Tee Work - take a plate and lay it down. Take a tee and place it on the back corner on the outside. Put up a net or next to a hitting tunnel and visualize where you want the ball to hit going to the opposite field. Have them separate the stride and swing first and work on taking a normal cut and seeing the ball going the other way.
Then to work on the complete swing take the tee and place it on the inside front corner and take the same swing. I think it's important to work both sides of the plate when doing drills.
Front toss - we use golf ball sized whiffle balls but you can use baseball sized ones or real balls behind an L screen. With this drill we get pretty close to the hitter to make sure of good pitches. We throw the ball about two inches off the plate and they work on taking the same cut as they did on the tee. Once again have them visualize where the ball is going and let them see it.
The balance for this drill is throw the pitch at the inside hip. Have them recognize the pitch and work on getting around.
Another aspect of this drill is once you work both corners have the pitcher hit all parts of the plate. The hitter needs to recognize the zone and lay off pitches that are off the plate.
To feed these pitches all you need is to do is throw underhand because you are going to be very close plus the whiffle balls don't travel very far - especially the golf ball sized one.
Short cage - get into a batting tunnel and set the screen about 15 - 20 feet away. Have the pitcher overhand throw the ball to the outside corner. Have them take pitches that aren't on the corner but drive the balls that are on the corner to the opposite field. Basically aim to the opposite side of the L screen.
Balance this up by hitting the inside corner the same way. Aim for the pull side of the L screen.
Down the middle of the plate have them hit the L screen.
In this drill it's important not to expand the zone like in the front toss drill.
At this point you can move onto the BP that floridafan described above. Once again have them visualize where they want the ball going and start developing discipline with the zone. One thing younger hitters don't realize is that they don't have to swing at everything in BP. This is where they learn the discipline to lay off pitches out of the zone.
Hopefully all this will help and others will be on to offer even more advice.
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