I rather suspect they are home as often as they were 20 years ago. And I wouldn’t be surprised if, by now, you can tweet 911.
I don’t know what kind of internet service you use but mine offers a bundle with basic home phone service for 15 a month. You can pay for more features like long distance service but just the basic is 15. I even have an old corded phone hooked up in case the electricity goes out. I wouldn’t trust Magic Jack. I never hear anything good about it.
Back when I was a youngin I babysat all the time without any sort of phone. We didn’t have one at our house until I was older. Somehow I managed not to damage anyone permanently. 
For that matter, could it be worth just picking up the cheapest little pre-paid mobile you can get with a few bucks credit on it and make sure it’s somewhere easily accessible when you’re out in case of emergency?
All I know is that all the VOIP providers like MagicJack and Vonage carry a warning about how they are not capable of handling 911 calls properly. There are plenty of situations (loss of power, unreliable internet) where you will not be able to rely on them. Thus, for your application, I would not recommend using VOIP.
The advice of a prepaid phone is good. As long as you have service, it doesn’t matter if you have minutes. Calls to 911 will still go through. Cellphones do handle 911 properly.
And, yes, your money would be better spent on a second charger for the phone, so that all calls, whether to 911 or to you can come from the same phone. That’s easier for even an adult to manage, let alone a 12-year-old kid.
You said your kid seems responsible enough to babysit but really only seem worried about the phone and the reason the phone is a problem is because he rarely uses it. My suggestion would be to either come up with a better phone solution for your house. Vonage has been suggested.
Or.
Get a second charger for your house and make sure (between you and mom) that the phone itself travels back and forth. That way he always has it on him and if the battery is low there’s a charger near by. If you don’t want to spring for a second charger just get him in the habit of plugging it in at night. Every non-smart phone I’ve had could easily go three days between charges, a week if could be turned off for 8 hours a day (like at school). Assuming he’s at mom’s at least 3 nights a week and she can make sure he keeps it plugged in and that it makes it to your house with him I’d think that would work.
If that’s not feasible, I’d make the jump to a regular landline or Vonage.
I recommend Cell-Phone Charger. It’s a $19.99 one-time purchase at pretty much any store (Wal-Mart, Best Buy, etc.) and works with a variety of existing cell phones. Just plug in your son’s cell phone and boom problem solved.
(Seriously…I’m an empathetic, warm-and-fuzzy guy usually. But I just can’t understand your insistence on buying some new gadget and paying extra when the solution is so obvious and requires minimal effort on everyone’s part.
Unless you want to buy MagicJack or some other VOIP system and are just looking for a reason to try it. In that case, by all means, try it out–no need to rationalize.)
Then I guess I’m not responsible enough to be a parent!