Since you did mention elk....
"....isnt a 7mm-08 a larger gun then a 30-06? Wouldent it kick harder?"
The 30-06 is the stronger cartridge.
"....she's only 120 lbs so she is recoil sesetive...."
Is this coming from her by experience or you by presumption? If she does try shooting some rifles of "more normal elk caliber" like a 30-06 then don't go hyping the "felt recoil" involved in advance. Let her decide what is too much. We had a 14 year old girl at 100 pounds take her elk two years ago with a 30-06 --- she didn't see what the fuss was all about.
OR, better yet,
Buy a nice little deer rifle (243ish)that is easy and fun to plink with to build up her confidence and experience level and use that for the deer hunt. Then when it is time to go elk hunting let her know part of the package is that she is going to have to step up her game to match the quarry. Then buy her an elk rifle. (Match size of the tools to the size of the job.)
"....size has nothing to with it. I am little and can handle more recoil than guys twice my size. I used to have a 30-06 when I weighed 90 lbs. I'm not going to say it didn't throw me around, but I shot it just fine.
"....What's wrong witht the 7mm Rem Mag? My old lady at 110 is shooting one. No brake, just a shoulder mounted recoil pad."
A couple of "counter-presumption" viewpoints, plus your wife has the weight advantage (though that don't matter much --- it is "the size of the fight in the dog, not the size of the dog in the fight" --- she may be more "non-recoil sensitive" than you appear to presume (based on what you've said).
IMO, try the 30-06 (or 30-06 equivalents)and if that isn't going to work then go to lesser if you must. If the next notch down (270, 7mm-08 etc)don't work, then maybe elk hunting isn't such a good idea, may just want to stick with deer and pick up a comfy deer rifle. I could get into weight of rifle, fit, weight and type ofbullet and size of load, technique, (brakes), etc, etc. but probably best to keep this one simple.