Take up drums at age 56?

I understand. Get more control between your left and right hand with rudiments. 
IME, the coordination on the kit that comes first is right hand, left hand, right leg. Coordination of the high hat is next, so dont worry too much.

And since you're a beginner, the instructor won't expect you to lay down a groove on the kit. He may start with hands only on high hat and snare... 1+2+3+4. Then add bass, etc.

$25 hour is great. I think I paid $20 in 1972.

So I've had the kit for about a month now. 'Practicing' at least an hour a day on most weekdays and weekends when I'm in town.

I'm practicing rudiments and limb independence exercises and working on some shuffles. Left hand still very lacking in precision and coordination compared to right.

I can do a basic shuffle but wanted to learn the Purdie shuffle. It just sounds so cool. But I'm not getting anywhere close even when it is broken down by YouTube instructors. A bit too soon I think. But it is a long term goal.

I've got a couple of simple retro style rock songs that I can play all the way through (JD McPherson). On one of them I saw the band live a few weeks ago and the drummer played it very different at the show than he does on the album.

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So now a question. I do most practice through the headphones but I've also got a computer audio system (two small ribbon speakers and a subwoofer with the amp in it.) I prefer this to the headphones when I can do it without disturbing anyone at home. It sounds okay but is obviously limited, but it was lying around so cost nothing.

I have access to an old beat up pair of B&W towers with a huge subwoofer along with an integrated Yamaha home theater system.

Any reason not to give those a try? The module on these drums has RCA output. I know a dedicated amp or PA would be better, but not ready to spend any money in that direction yet.

Finally, how should I position such a system. On the drumming videos most drummers have a PA system behind them.....but I'm not performing for anyone so I would assume I'd just have it facing me? 

@n80, the way to strengthen your left hand is to lead with it. If you are practicing rudiments (do it on a practice pad, rather than sitting at your set), play the "R" parts with your left hand, the "L" with your right. Set your kit up backwards, forcing yourself to play left handed and footed. It will feel very awkward and you'll suck at it, but it will bring your left hand and foot closer to your right. Did you know that although Ringo set-up and played right handed, on his fills he led with his left hand? Weird!

Leading with the left hand is a great way to practice.

You can strengthen your left wrist by starting slowly on the practice pad using only your left. Do single strokes, doubles, triplets and keep proper form. 

@n80, I just recalled a piece of advice from an old master I read years ago: when going about your everyday life activities, use your weak hand instead of your strong one. Brushing your teeth, opening doors, cooking, even try writing with your lesser hand. Using it more will develop it's abilities, the same way your better hand developed.