What is the problem with the controls for the dragon?
I played the Xbox version of the game. At the start of the zeppelin escort a couple dragon skills are upgraded or added, and the hotkeys changed, but I could pause the game and re-assign the hokeys pretty much the way I had them in the D2:ED section of the game.
Larian is working on a patch for DKS to add the Developer Mode (which is the only difference in D2:DC).
If changing the hotkeys is the issue, then from a couple different topics:
How are you assigning skills to quickslots? There are a couple of ways:
1) Keep the numerical key on your keyboard pressed for +- 2 seconds.
2) In pause mode, right click on the slot you want to quickmap.
3) In the skill screen, drag the skill icon to the quickslot.
Which of these options are you using and can you try the others?
It'd help which skill you were trying to hotkey because, not all skills are hotkeyable. For the ones that are, you Left-Drag the skill into one of the slots and click when the slot lights up. From my experience, those slots don't become active (light up) unless you aim towards the very bottom of the slots. I think they did that so that you couldn't accidentally move something out of the bar. They must never have heard of "Locking" the action bar.