I like stability training of the core for swimmers. Think plank and bridge progressions. You want the core to be stable where there isn’t a lot of twisting side to side. You want the stroke to be efficient regardless of the stroke being swum. This is specific to your question of what core work could be done to enhance swim training.
You also want to strengthen the back, chest and shoulders in all ranges of motion. I like tubing for this and often will use tubing with additional weight from dumbells. It more closely mimics the push and pull of the water. I also try to have clients, as well as myself, keep their hands lose when gripping the weights when strength training for a swim as to mimic hand formation in the pool.
Of course, nothing compensates for time in the pool, but core and strength training can help make a swimmer more efficient.
Resistance training is certainly going to go a long ways in swimming, but let me just point out a few areas to concentrate on.
The shoulders and rotator cuff muscles – These are small muscles that fatigue quickly as they’re not used much in daily life compared to swimming, so it’s very important to train them in both strength and endurance. Any direction your shoulder moves, you should train that movement.
Glutes and hamstrings – In my experience, most of the population is strong in the quadriceps but lacks the balance in the posterior chain, that is the back side. You would do well to perform hip extension exercises, and total body lifts like deadlifts and squats, though you should consult a professional if you are not one yourself as poor technique can quickly lead to injury.
Chest and back – Triceps and biceps are not as important as they are the prime movers of the elbow. Swimmers’ movements occur primarily at the shoulder. The upper and middle back and often very neglected areas of the body.
Core stability – Anti-rotation and dynamic stability exercises will strength the core and prevent energy leaks, making each stroke more efficient. Also note, consider the whole “core” not simply just the abdominals and obliques.
There are many great suggestions above! I would also like to add that one of the keys to an efficient swim stroke is shoulder and thoracic spine mobility. A combination of soft tissue work with a foam roller or other tool, stretches and joint mobilization exercises should vastly improve mechanics in the pool.
There are many ways to enhance performance in all athletics. What is really important is to be able to uncover weaknesses and imbalances that are detrimental to performance. While all athletic activity is not the same, many of the necessary strength area are the same. Training should focus on the entire body and bring deficiencies upto strength and into balance. I wish I could find a way to help more, but the presence of the fitness professional is absolute necessary to get the best results and the safest results.
Things that I can recommend are working on stability/balance (literal balance, standing on one foot, etc.), strengthening the core (abdominals, spinal muscles, shoulders, hips, etc.), and getting enough rest and recovery time.