Many strength and conditioning programs for sports are outdated already. For example, athletes would normally make you do hundreds repetitions, which is not only unnecessary, but is also counterproductive) and tends to over train you. In some aspect it is good for your GPP or basic conditioning but that time could have been dedicated to power training, endurance, etc.
Some moves are very complex and you cannot learn them in one lesson, e.g. Weightlifting moves, plyometrics not to mention structuring them to fit your martial arts training. A smart strength coach evaluates your sport. Then studies the attributes of your sport . And the program will depend on what is trainable, what is needed and build up your base.
skill training and strength training should be separate. In some sports, it is thought that by just adding some weight to a move, it will automatically improve the technique. The problem here is that the specific movement would use a different set of muscles if done slowly, thus when the resistance is removed, the skill is not transferred into fighting. Also the problem with that is it screws up the way you recruit your muscles thus affecting your accuracy.
Sports have different attributes such as: agility, speed, endurance, skill, technique and strength. It would be best of you can get somebody to train you in the different aspects of your chosen sport. Ask the help of your sports coach for your technique and skill. Hire a strength and conditioning coach to train you in strength and conditioning.
A lot of sports enthusiasts have forgotten the strength and conditioning aspects of sport. It was the former Soviet bloc who was successful in integrating strength training to their sports training. Then the world followed. Time for the local sports associations in the country to follow their example. Strength training for sports was never done right. They do bazzilion reps and get sore then blame strength training for making them stiff and slow. Totally scrapping strength training. Get a knowledgeable strength coach and you will improve your strength and power.