Step #1: Have your wife shoot your 30-06 and see how it feels for her. There's no substitute for real world experimentation - if she can handle the recoil of a 30-06, there's no need to go looking for anything smaller or lighter recoiling. Nothing I'll say below matters if she can handle your 30-06 comfortably.
Keep in mind: Elk are the hardest to kill, and most likely the one you'll hunt the least. Saying "Pronghorn, deer, and elk" sounds easy, but that spans a gap between about 100lbs and 600lbs, dictating disparate needs in a rifle to hunt them. Sure, an elk rifle will kill deer and pronghorn, but it'll carry a lot of extra recoil to do it. Couple with that your likelihood to hunt each species. Deer hunts are cheap and easy, even out of state. Antelope and elk, not so much. Sure, there ARE states where you can DIY hunt elk with OTC tags, but they're not cheap, and guided hunts are assuredly more productive in quantity and quality. For most folks hunting as non-residents - especially couples - elk hunts only happen once or twice every 10yrs. So your wife might be better served to get a deer and pronghorn rifle that's just enough for elk, OR, let her use your 30-06 on those rare elk opportunities, OR get her two rifles.
ALSO - Keep in mind: Even within the same model, not all cartridges have the same weight or balance, so a 308win might feel very different to her than a 7mm Rem Mag even in the same model. Short action rifles tend to be the lightest, and often have the shortest barrels, typically 22". Long action standard cartridges often weigh about 1/2lb heavier than short action versions of the same model, with 22-24" barrels. Long action Magnum cartridges often weigh another 1/4 to 1/2lb heavier, and typically come in 24-26" barrels - So a 7mm Rem Mag might be 2-4" longer and a full pound heavier than the SAME MODEL in 308win. Remington - typically one of the lighter models on the market = highest recoiling - doesn't follow that trend as tightly, there's only about 1/2-3/4lb between their short action and long action magnum rifles - meaning their 7mm RM will tend to have a lot more recoil than makers like Savage or Ruger. It's a good idea to let her hold the actual rifles, not just one representative.
If the 30-06 proves to be too much for her, then you can consider this ranking:
308win = ~16.5 ft.lbs. Free Recoil Energy (8.5lb scoped rifle w/ 150grn load at 2850fps)
270win = ~18 ft.lbs. FRE (9lb scoped rifle w/ 130grn load at 3050fps)
30-06 = ~20 ft.lbs. FRE (9lb scoped rifle w/ 150grn load at 2950fps)
7mm RM = ~22 ft.lbs. FRE (9.5lb scoped rifle w/ 140grn load at 3100fps)
I'd recommend, however, that the 243win is quite possibly the most efficient deer hunting cartridge on the market. A 243win proper deer hunting load will only have around ~11.5 ft.lbs. of free recoil energy out of a "standard" short action rifle. It's on the bottom end for elk, and not legal in all states, but if you're open to having 2 rifles for her, or letting her use your 30-06 on rare elk hunts, the 243 is a great option.
If you're dead set on only one rifle for her and not using your 30-06, then look a little heavier than the 243win. The 7-08rem and 25-06 are good short and long action options, respectively, for deer and occasional elk. More punch on the business end, but still a big reduction compared to the 30-06. Either of these are effective elk rifles at moderate ranges.
Comparatively - if she shoots your 30-06 as a benchmark to set the standard:
243win = 58% of the 30-06 recoil = kicks a little over half as much
7-08rem = 75% of 30-06 recoil = big reduction
25-06 = 75% of 30-06 = big reduction
308win = 83% of 30-06 recoil = significant reduction
270win = 91% of 30-06 recoil = knocks the edge off, but not much
30-06 = your standard that she compares against
7 RM = 110% of 30-06 recoil = incrementally more recoil above an already stiff kicker
I'd personally look hardest at the 7-08 and 25-06 for a low recoil deer, pronghorn, and occasional elk rifle.