Not sure if this will help, and I also posted a thread on this a while ago, but I would try the one-armed drills for help in this. In the thread I posted on this, there were 2 different versions that were discussed, one advocated by Charles and the other by Suzanne. I wound up focussing on Suzanne's because I think it is easier to learn and helps perhaps more with the kind of issues you are talking about. For more than a month now, I have been spending about half of my workouts doing one-armed drills, and I keep doing them, because I am still learning things from them and I think my technique is still benefitting from them. The question I keep asking myself is why they are so helpful, and this is a little hard to answer, which makes it all the more mysterious. Here are my thoughts on this, which are hopefully relevant to the question you are asking.
With two armed swimming, we can use the weight of our recovering arm to initiate body rotation, especially because it is out of the water and thus "weighs more". With one-armed swimming, you lose that help in body rotation on one side, and this means that you are going to have to work more with hip rotation to compensate for this loss. If you spend enough time doing this, it forces you to start concentrating more on initiating body rotation with your hips and how to coordinate it with your arms. An additional help is the fact that the one-armed drills seem to slow the whole process down. When I am doing these drills, I often feel as if I am watching my own swimming in slow motion. When you swim with two arms, you can slow the stroke rate down, but the weight shift (the critical point where coordination between the hips and the arms occurs) still seems to happen rather quickly. In contrast, I feel like this process happens more slowly with the one-armed drill, and this helps me with the coordination issues you raised. I slow the process down even further by doing the one-armed drill with my hand in a closed fist, which I recommend.
There is more discussion on how to do these drills in the thread I mentioned. Two key learnings for me were (1) How to coordinate body rotation with the bobbing motion caused by your recovering arm and (2) How to feel the kick and rotate as a sort of undulation, which powers the stroke.
I hope all of this is at least somewhat relevant! Good luck!