I know that stage 2 is more about introducing fly kick. And you can do it in a number of ways. I find the easiest way of introducing fly kick is to simply demonstrate it with the hands by the hips and kicking with the face in the water.
The tricky part is teaching the arms, and then connecting them to the kick, or hips, and finally the breathing.
Break everything into stages.
Kick first with a good body roll starting at the chest and flowing through the hips and feet.
Then train the arms independently without a kick. Do the MOTION.
Finally, add the kick without breathing.
Sneak in a breath. As the arms push down breathe, then get under before your hands return to 11.
3 Different Fly Kick Drill
Do the first 3 like the pictures (1 each). Last one do “correct”
First line is very flat, barely moving.
Second line is generally what fly kick should be
Last line is super exaggerated like dolphin dives from bottom, straight up to surface.
3 x SL + 2 Fly arms with 1 Fly kick right at the end when arms return to 11.
Fly arms review
As hands move under body, hips should push down, or forward to meet them.
As hands swing wide to recover back into position 11, the hips should rise, or push backwards.
3 x SL + no K + 2 FLY strokes
No kicking throughout. Glide on SL first, then at the surface move the arms in the fly motion.
Okay for the recovery, from hips to 11 to push the swimmer backwards.
Thumbs aim down, and should be only part of hand touching water.
Arms do not recover UP, or above the body. Natural to the sides and forward motion.
2 x 25 Swim fly for 2 strokes, then only fly kick the rest of the 25 With FINS.
No breathing on the swim part. They can breathe whenever they want on the kick.
Goal is to do a short distance of swimming. SL with fly kicks, then at surface do two fly strokes while kicking. Then put hands in soldier and kick body dolphin or fly kick the rest of the 25.