You've got two unquantifiables here, "under load" and "smooth". Depending on what your/hers personal opinion about these are, you might never get a satisfying result. The things you can do:
1) take a look at the chainrings, ones that are "ramped" and "pinned" are supposed to offer better shifting.
2) check your cabling and try to get a feel for the derailer spring. A really clean routing of the cable will lead to less flex/compression of cable routing, which should help with snappier upshifts. A strong derailer return spring should help with downshifts.
3) some chains are supposed to shift better than others. Shop around a little.

But above all, try some schooling. A lot of her problems would go away if she rode with a bit of advance planning. A bike with a triple front usually have plenty of repeat gear ratios, so the trick when approaching a climb is to do a double shift. Drop the front one ring and drop the rear 1-2 gears. That'll leave your cadence just about unaffected, and you'll be on the right ring when you hit the incline.

The least part of the equation is probably the shifter, unless she's having trouble pushing/turning on it hard enough. When you do a front upshift you're basically pulling directly on the cable and with that the derailer. If her thumb is too weak then maybe a grip shift or a downtube shifter mounted on a Thumbie can help. Front downshifts happens courtesy of the derailer return spring, so not mufh influence of the shifter there.