That video, to me, shows a problem entirely with the toilet itself, and zero to do with the house plumbing. That bubble is coming out of the siphon jet hole, and you're not getting much action from the siphon jet during the flush. That suggests that something may have stuck up in there during the plunging, or something's crusty up in there, but instead of a rush of water coming out of there as water dumps from the tank to the bowl, you're getting a bubble and a little bit of bubbly flow (and more water than usual going through the rim holes rather than out the siphon jet).
From the toilet cutaway below, you can see that when you flush and water rushes from the tank through the connection to the bowl, gravity causes part of it to run to the rim holes, and part of it is diverted down to the siphon jet hole ("G" in the diagram) to start and continue the siphon that evacuates the bowl. Something is blocking that from happening properly.
If Mom and Sis come back with a more-modern comfort-height toilet, you should be in business. A lot of us like Totos, but if they are going to HD, the HD $99 elongated comfort height toilet actually performs quite well. I helped a bar-owner friend install it in her Men's Room well over a year ago now, and to my amazement it's still chugging along just fine despite a lot of abuse.
http://www.homedepot.com/p/Glacier-...sh-Elongated-Toilet-in-White-N2428E/204074796 Personally, I would be wary of their 1-gallon-per-flush model, but the 1.28gpf elongated -- at least the version we installed, and HD's toilets change frequently -- works fine. It flushes well and doesn't clog easily. It has kept on working despite the Super-Cheapo-looking fill valve and flimsy-looking flush valve. I thought that I would be finding myself replacing one or both within a few months, but nope, they both still work fine despite probably 100 flushes a day. (My thinking was that someone would smash or crack the thing, requiring replacement, at virtually any time, so I focused on replacement cost more than longevity of the moving parts in the tank. As it turned out, it hasn't been destroyed yet, and keeps on chugging.)
Your efforts and concern should make your Mom proud.
Good luck.
