Hind leg at trot; outside hand

With our busy competition calendar and my lessons limited to weekends, it's been a while since I've had a flat lesson with Shannon.  Yesterday we had a very satisfying one.  The lesson before that - which I never had time to recap - Shannon suggested a hip exercise, which I have remembered to do twice.  It was swinging it forward and back, and then across, to stretch out both directions of movement.
In yesterday's lesson, there were a few themes:  Keep the contact with my outside hand - especially with the left hand, I like to cross it over his neck still; For lateral work, keep the weight balanced and even - going to the right, I put all my weight in my left hip and my left leg and then the right leg sticks uselessly out like a rudder; and then we worked on feeling when the outside hind leg is lifting.  At the walk, it is when your inside hip is moving forward, and at the trot, it is when you are sitting in the posting trot - when his inside shoulder moves forward. 
The outside hand is huge - it is why on sharp turns, especially to the right - I lose it.  That left hand goes limp or crosses over, so I have to do a big sweeping turn off his face instead of through his body.  We practiced doing 5 loop serpentines, and that helped a lot to feel how different each side is and how much smoother the turn is when I ride him into the outside hand.
Shannon also checked my warm up and said the long and low is good, so long as his head is going down - not forward and out, but that I need to ride it more forward (instead of dragging his feet around), and not to warm up like that the entire ride, but to do a few laps then get to work.
The other thing was to make sure we are set up for transitions - he should be in the Major Beale round frame, ready to canter, and straight - not go ahead and lunge for the transition without preparing.