Write yourself a checklist of things that need to be done while hitching up and preparing for towing. Then, make yourself use it, avoiding distractions, every time.
No checklist is perfect when first written. Try it out, then move items around so that they flow in order as you walk around your rig. Realize that it's better to use it as a "check" list than as a "do" list. When you think you have everything done, that's the time to pick up the checklist and do one last walk-around.
First few trips are a learning curve, but that's soon over as you get used to the routine. Enjoy your new Airstream!