What advice or drills would people offer to a young batter who drops their back hip when playing forward in defence or attack?

Such a common problem with a few different issues normally associated, let's try and cover a couple of them. First thing I normally check is for an even distribution of weight through each foot in their stance and their head centered. May as well start in a balance position. I also find that batters that have this concern have a bottom hand dominant grip, its low on the handle and holds the bat tightly. So I encourage them to loosen this off (squash ball as per Gilchrist in 2007 World Cup works a treat) as well as keeping hands together and more to the top of the handle rather than the bottom, helps to achieve a full swing of the bat.

To me one the keys of transferring weight forward when playing front foot shots is place an emphasis on the lead shoulder and use it as the key body part for the batter to be aware of. Point that shoulder in the direction they want to hit the ball, the head follows automatically and their weight transference is then in the direction of the shot. Its hard to achieve that if the weight is dropping into the back hip. If they get that right you are well on your way to solving the issue.

What can also be useful is to "back-chain" the skill. Place the batter in the end position of the shot, i.e. full follow through with hands up and over the front shoulder. Drop balls from in front and to the side of the batter and ask them to step forward and finish their shot in that position. You can vary their hitting direction from midoff to mid on direction with the emphasis on the front should alignment position.

Then its a matter of repetition, patience and appropriate positive re-enforcement in the coach's verbal communication. The more balls they have hit with their old method the more they need to hit to embed the change.

Keep it simple to start with. Most players who do this are looking for extra power at execution and they buckle the back knee forcing the hip to drop.
Use a drill where the batter pushes his eyes to the line of the ball this will entice the keft shoulder to hold position and the weight to come through the front knee. Simple but effective to start with.