I did not read the whole thread...
But I have a couple of inputs/thoughts.
1) one of the larger puppy playpens, tacked down with a couple of tent stakes would put the kids someplace secure (assuming you can see them and verbally stop them from trying to escape) yet free to play with toys etc. Plus it would be easily transportable. If you made a game out of, "You get to be puppies today!" they might even like it.
2) One barn I boarded at when I was a teenager and had no need for it, had the GREATEST thing. They had a full fenced playyard. It was about 10x30 feet, had some large playground type toys in it, wood chips on the gound, seven foot tall sides with a wire roof, and a door that latched from the outside. It was easily seen from the grooming area and the outdoor arena.
I have never seen any other stable that had one, but it was worth its weight in gold. Moms could drop the kids off to play, with goodies, smaller toys, juice boxes, and then not just play for a minute, but actually ride thier horse.
If finances are ok, and you like the stable enough that you are goign to be there long term, you might talk to the stable owner about putting in such a thing... maybe you could pay for some of the costs/do some of the labor etc. But I know that the stable would find a lot of moms would flock to them because of it.