The 6.8 will take deer. It is about the same as a 30-30. They compare closely with 130 grain bullets. Bullet construction and placement are key as always and limit the distance to 200 yards or so. The G2 with a 23" barrel will not be that much heavier than the superlite. It depends on the stock you use on the G2. If you use a plastic stock/fore end it may be about the same. They are both light rifles. With that said I do not think the recoil is going to to be less than the 243. A 6mm 100 grain bullet runs some where around 2900 fps in a 243. The 130 grain bullet will run around 2400 - 2500 fps. Muzzle energy for the 243 will be about 1867 ft/lbs with a 100 grain bullet; for the 6.8 it would be 1662 ft/lbs for 2400fps and 130 grain bullet. Less but not a whole lot. The 243 with 85 grain bullets and 2600fps has about 1275 ft/lbs energy. I would think that if you limit the distance of the shot to no more than 150 yards the 243 with 85 grain bullets will do the job. You must consider bullet construction and placement again. Stock shape/fit, recoil pad, weight of the rifle, etc can make up the difference. As a rule of thumb 1000 ft/lbs is considered minimum for deer. No one can tell you what your wife will tolerate. There are always trade offs when weight and recoil are considered. I have found that when shooting at the range recoil can be brutal, but in the field when shooting at game the recoil is hardly noticeable. I have a 6.5 pound 12 gauge shot gun that about rips off my shoulder when sighting in (three shots will bruise my shoulder), but when I shoot at something important I do not feel it at all. Maybe you could load up lighter loads for her at the range to practice with and load up heavier ones for the actual hunt.??
