Separately, I bought this mini-trampoline, a Needak fitness rebounder wtf, to have something to redirect T. to when he jumps on the bed or the couch. The jumping on the couch with the pillows removed is really damaging the couch and upsetting R. As a redirection, it seems to work, but T. has been ill and less active so we won't know for sure until he's over the cold/croup thing he's got.
Today, I decided I'd try that whole jogging-on-rebounder thing that I saw mentioned online. I'd been on and off it for a few minutes at a time since it arrived, and I thought I had a pretty decent sense of where I was on it so I wouldn't inadvertantly get too far off center (I didn't buy the stabilizer bar because, as noted previously, that looks like a toddler tooth accident waiting to happen). It took a little while to get the hang of running in place on it, and I had to adjust my pace a few times, but it really can be aerobic, it really is more or less no impact, and it really, really, really does weird things to your stabilizer muscles and, also, one's pelvic floor (yeah, so, more kegels are good. Also, pee before bouncing).
I have _no_ mortal clue how many calories this thing burns (altho I'm going to attempt to find out ETA: depending on weight and how energetically you use it, approximately the amount you'd burn at a brisk walk or a slow job, so, 300-400/hour), but it is _very_ fun and does provide at least a little exercise in a safe-around-small-children kind of way. Which a treadmill is a little questionable, in terms of little fingers getting caught in a scary ugly way.
ETA: Needak seems to have a weight limit of 300 pounds, but may have options for people who weigh more. Cheaper rebounders have weight limits more in the 200 range, and reviews suggest even these limits are optimistic. Needak warrants different parts of the device for different lengths of time; the springs apparently are warranted for 2 years.