It takes time to develop your cast. Backyard casting is valuable, but so is casting out on the water. I started off with 15 minute or so sessions fly fishing water and structure where I had caught fish previously on arties. After the session, I'd take a break and fish conventionally and then later resume the fly casting. I think it's important to get some takes and fight some fish fairly earlier in the process to keep up interest. In other words, don't feel like you need a perfect cast to wait to go fishing? It's real easy to press too hard at first wanting to get up to speed over night. Real on the water time helps develop the line management skills vital to bringing fish to hand. For me, I had to make a commitment to get through the early learning stages. It also helped me to open my mind to the learning process and discard any preconceptions I might have had about fly fishing and casting.
I'm at the point now where I look at my loops and try subtle changes to arm angles and force to see how it affects the loop. Personally, I would put very little effort at this point in anything like trying to double haul. If you want to add and perfect that skill later in the process go ahead, but my experience is that it isn't necessary where I fish to be successful in bringing fish to hand.
Anyway, good luck. Bill Gammel youtube has some good videos on the cast. Fly fishing has been the most fun I have ever had fishing. It has become a part of me more than any other way of fishing.