I just wanted to thank everyone who took the time to respond here. What has really resonated with my experience is the need to skate, skate, skate.
I picked up a pair of skates and a LTS class for the first time in Nov. 2013. I was 33 years old, and had never been on skates EVER. Let me also note that I'm muscular and enjoy activities like weight lifting, but anything that requires balance and coordination is a challenge for me.
For the first, say, 8 months, I only skated at our weekly LTS classes. I tried a few public sessions, but for whatever reason, those days were the ones that every person in Raleigh decided to ice skate. (Shoulder to shoulder, seriously, for months, so I didn't get much in the way of skating outside of my LTS class. I felt too intimidated and out of control to try to learn to skate with 100 other people and a bunch of tiny children whizzing about.)
So for about 8 months, I halfheartedly attended skate school classes and went to a few public skates here and there, maybe skating 3-4 times/month. I would go whole months and not skate at all. I bought my hockey gear in March 2014 because I thought the extra padding would give me some confidence. I LOVED the stick and puck sessions, though I still couldn't skate very well. I enrolled in a LTP instead of a LTS. I thought that by shifting the focus from skating to playing I would relax and the skating would come, but that didn't happen. I was skating 3-4 times a month and not getting better. And I was angry about not getting better, even though I had no reason to be getting better. Dumb.
Fast forward to January of 2015, when I decided that I either needed to go all in or give it up. The turning point was a scrimmage at a hockey clinic in December.Though I was clearly the worst skater there, I could still do what most everyone else did, even if I had to modify. It was so much fun to just participate.
So I enrolled in another LTS, this time with a figure skating coach. (That's been an adventure.) I'm trying to go to morning public skates 2-3 times a week in addition to my weekly class. I feel so much more comfortable on the ice. I don't know that I would have gotten back into LTS if I hadn't read these posts that said that skating was step one. I had kind of elided that part of hockey, thinking that I would pick up what I needed as I learned to play.
tl;dr: Thanks for posting. Your advice gave me the push I needed to focus more clearly on my skating.