Hello again, everyone. I've ridden I think four times since that lesson, and he's pulled the refusing-to-walk-on thing every time, but always half-heartedly, not like the major fit he threw last Wednesday. The first ride after the lesson, he did it pretty close to the beginning and I tried to get him to move on, but I didn't feel related to have the kind of fight I did with the trainer there (I've still never been on a horse when it reared, and I was nervous) so I got off, worked him on the lunge line and got back on. It went well after that.
The other times he did it this week, all it took was a smack with the reins (they're soft reins — it didn't hurt him, just got his attention) and some firm steering and he gave up. I've been working on the things we did with the trainer but not for as long a session, and it's going well.
I think it's just exactly what you all have said: he listens usually, but I don't have his full attention, so when there's a distraction, I lose him. I definitely feel like we're going to get through it, though.
Another rider ( the owner if the horse I leased before I got Sam) said something that made sense, too. She said horses follow their leaders, so if you're riding and a horse tries to follow other horses out if the arena or focuses on anything but you, you're not the leader, and when you are, the horse looks to you for security and therefore would rather follow what you're asking than the other horses. As I've said, leadership is not natural for me, but I'm really hoping I can get there!
"...and may your life be filled with good horses." — Buck Brannaman