I've been checking in on this thread all day and trying to squeeze in time to respond (busy day at work) -- and was glad to see that all the DIS dog experts were already saying what I wanted to say!
OP, you obviously care very much about the dog that is driving you to your "wits end." Much praise to you for taking in this high energy, anxious, *troublesome* pooch.
I was going to say earlier that there would be absolutely no shame in rehoming him as you obviously have your hands full with the children -- but then read the bit about having to return him to the previous owner. Not good!
My big worry here is that you will invest in a doggy treadmill for major $$$ and the dog will not use it. You did say he was a scared and anxious dog? Do you have the time to invest in training him to use it? You may get stuck with an expensive piece of dog equipment and be back to square 1.
Here are a couple of other ideas:
1. Look into dog walkers. Do you know anyone that walks their dogs and might take your dog along for free? Could a specific breed rescue put you in touch with someone who could help you out? Could your vet recommend someone that would not be too expensive just to get the ants out of your dog's pants?
2. Training is fantastic. I can't recommend it too highly. Could you do obedience training once a week with some of the kids? It is really fun and can lead to fly ball or agility. Involve the kids, learn tricks, get a happy and challenged dog. Practicing at home may help deal with the energy level.
3. Our old amazingly good trainer (and my good friend) moved to PA from MA a while back. I loved her because she trained me to train my dogs for myself! To be clear -- I'm not trying to drum up business for her because I know she is fully booked right now. She also only trains one-on-one these days within a very small radius of her home because she is also caring for her elderly Mom -- but she might be able to recommend a trainer/walker for you. Please PM me if you would like me to ask her on your behalf or put you in touch with her directly.
Good luck!