You are on the right track.

It sounds like he is overbending his neck rather than quickening the hind legs and keep them under his body. Remember, the body has to be straight in leg yield. Do you have a long whip? If so, you can try to touch your horse on the right hind to see of you can quicken his hind end to keep up with the rest of his body. You don't need to hit him, just tickle him with the whip in different spots - behind your leg, on his bum, until you find a spot where the whip will encourage him over. So it would be: slight half-halt - touch, tickle or light tap/tap with the whip - quickening and lateral movement of the hind legs - praise - repeat.

Once he gets the idea to quicken, you can try with your leg and body with the same lightness as you do to the right. It's better in my mind than asking harder with you leg.

Also, watch this video advice for fixing lateral movements from Olympian Belinda Trussell:

http://www.barnmice.com/video/ask-an-olympian-week-15

F+, I haven't heard that before about the front and back legs. As I understand it, the shoulder-in is a preparatory exercise for collection and it does focus on the hind legs and the horse closing up. How was it explained to you?

Well it's not. It's more for leightenings. The front legs now can move out of the way. You'r moving the front legs around each other and the hind is more facing the direction you are going.

Most oftentimes resistances in LY are riders lack of timing. If a horse is tossing its head and resistance to the reins look to the hands (like fixed and low). Aids must be pulsed.

Second look to the degree of LY, at the beginning it should be mostly forward/sideways and 'inflating the outside rein' with pulses from the inside leg. An easier way to initially present LY is to do so as part of a spiral, and 'enlarge' one side of the circle with these pulsations. This 'yielding to the leg' (vs the hand) with a degree of bend makes it much easier.

Least we forget LY is not a classical exercise (because it has no bend only flexion at the atlas), and if done should be more presented in walk (perhaps only for some more downhill built horses) first, then in trot.

The rider has to first look at how/when/where they are applying the aids, 99% of resistances are those of the rider. Initially a rider might ask with the inside leg behind the girth, but this should be short-lived. The inside leg can say move-over (a couple of actions coordinated with the inside leg), but then the outside leg just say go-straight (on the inside track perhaps). It is MUCH easier to present LY head to the wall for a few strides (and traditionally this was the ONLY way it was done south of scandanavia).

Are you saying the position of the leg aids are opposite?  Yep, can be.  It is the ONE exercise on which many people disagree (I had a student who did a comparision of 25 authors on it as well).  The reasoning for having the inside leg closer to the girth and outside leg back is because it is very traditional within a very untraditional exercise, and that feeds into the future training of the horse.  And the LY does work without the extremes of inside leg back in most cases, so the rider/horse do not have to relearn aids later.