That's a good amount of practice, so you should see progress every week, I'd think. The more you push yourself to do the things that are harder for you, the more quickly you will get your legs to figure it out.
I started playing hockey about 6 months after I started working on my skating, and I was able to do alright. It's been about a year for me now, and while I'm still not as fast as I'd like to be, the transitions just about automatic, which I think is one of the hardest parts. I'm signed up for an intermediate hockey class which will start next week, and I'm curious to finally have some formal instruction and see how I can improve.
The skating lessons should help a lot. When you're at public skate, make sure you're not just going in circles - hockey skating has a lot of changing directions fast. When I practice I like to zig-zag alternating backwards and forwards all around the rink. Or do the figure eights where you're always facing one direction and have to keep doing transitions. I often see new hockey players just doing laps and I think it's kind of a waste of ice time. Put on some padding and force yourself to do the hard stuff and you'll be a great skater in no time.