I have the tandem TAB, hitched behind my regular tandem. There is definitely enough moment-arm and play for the tandem-TAB to swing things around. Tiring and stressfull.
I weigh 190lbs, child stoker is 32 lbs, tandem is 40-45 lbs counting racks with diaperbag and lunch. TAB stoker is ~50lbs, baby-seat occupant is ~25lbs.
One thing that helped was my wife watching, and identifying when the bike lurched. It wasn't the younger kids leaning or turning, it was the TAB-captain switching from coasting to pedalling with a lurch and lean that really rocked the bikes. We're trying to get her to transition more smoothly.
I think I removed the rear cranks so that the baby seat could go lower, but forget exactly how that works.
One thing I noticed pulling single TAB's behind bikes was significant stability differences based on the bike. Pulling single-TAB behind my road bike, which attached high and had a steep seat-tube angle, was much less steady than behind my Mtn bike which attached lower due to the sloping top tube and has a more slack seat-tube. No idea which of those effects caused the stability difference.