Most all skis have a tip that is the widest, then a few have a tail that is maybe 10 mm narrower than the tip (some alot lower too). The waist of the ski, under foot is the narrowest part. The numbers usually read something like 100-64-94 or a wider one at 110-66-98 and then a radius for the turniest for a groomer, all mountain, carving ski (this is just a few examples for a range). Fat skis (good for powder since they have more surface area) are now at 120-90-115 range. If you ski in the east or midwest then powder skis may not be the best for you at all, people make them work on groomed trails but they may take some time to get used to. 20 year old skis were maybe 84-80 max.
The smaller the radius the shorter the turns and turns are
with a ski that is longer and a higher radius.
Slalom skis (watch the racers some time on OLN or the upcoming Olympics) are turning around gates much faster than a longer giant slalom. But you are not racing so you may be best with something that is in between the highest GS ski and the lowest Slalom ski- 15 to 18 maybe for the radius. This is where the demoing or rentals (not the beginner short rental skis, a step or 2 up from them) come into play. If you ski on something you like you can then start shopping for that model or something similar.
You state your wife seems to be progressing faster than you, people do learn or can visualize things differently, or she could have a better pair of skis than your "Race" skis and therefore able to turn more freely. Some take 3 or 4 lessons before they are even comfortable getting off the bunny hill, others are may feel ready after 1 lesson, due to a good teacher, athletic ability, or lack of fear.
"Race" skis are not for everyone- if they truely are a race model- they are probably a very stiff ski that is harder to turn at a slower cruising the mountain with the family speed. It is not always the money (they could have been cheap for a reason) but the "deal". Last years or even 2 years ago old stock could be a deal only if it is in your length and meets your needs. Otherwise you may be better off looking for scratched and cosmetically flawed rental skis that are in your length and skiing ability to enjoy skiing and progressing.
Lessons (at least 1 or 2) as others have stated can help greatly. The shaped ski is designed to be put on edge to carve not skidded around on the bases. The stance is a little differnent than 15 years ago (called by most old school- knees together, skis close together and weighting and unweighting the body to get the turn made) A good set of 2 or even 3 year old (new or well taken care of used skis) would be better than a pair of nonshaped skis in improving the skiing and turns. After all speed control is all about completing turns to check the gravity of the fall line. Read up on the gear discussions, get the Ski and Skiing fall gear guides (go to the library if you can't find the info on line) and read what they have to say about the different categories of skis for the various ability skiers out there. For now stay away from anything that states race stock or world cup expert skier, until you progress and are looking for that type of ski in your quiver of skis to take to the mountain.
You can read this pretty concise guide to the issues of shopping for skis:http://www.skiernet.com/ski-buyers-guide.html