The main factor, is that your partner is a smaller, less powerful rider, and there's only so much you can do to her bike to make up for that disadvantage.
IIf you're both doing the same ride, in the same amount of time, then you're both doing the same amount of Work. The difference, is that it may be 90% of the maximum effort she could do, but only 70% of yours. Unless you're dragging a sled, or something, you will be stronger and therefore faster than her.
It takes a certain amount of power to cruise at your ~13 mph average, and the bike itself absorbs only a small part of that (unless it's in very poor repair). On level ground, bike weight has no effect on cruising speed; now, climbing or turning, it does, but at 12 mph on road routes, it's marginal at best.
Going to a larger wheel wouldn't really change things either; it might go 10% farther per revolution, but it takes more effort to make that revolution, so you shift into a lower gear, and it all washes out. 70 gear inches is 70 gear inches, whether it's a 700c, 26er or 20" mini-velo, if I ride 70", at the same cadence and level of exertion, then I'll go about the same speed regardless of what size the wheel is.
Ignoring component level (quality) it may be that her MTB just doesn't have the right spread of gears for extended cruising, but might also be that she's not using them optimally: grinding on the biggest gear, trying to keep up, and wearing herself out, when she could shift up a couple gears and turning a higher cadence at a lower peak effort.
13-15" -frame MTBs and hybrids from the major brands like TREK, Specialized and Cannondale are out there, as are 48-50cm road bikes, in full 'adult spec' ie; not heavy "budget" kids' bikes (Cannondale CAAD-2's are remarkably light if you can find one)