Ben I would like to echo the suggestion Bigbulls made and toss another vote in the hat for a bolt action 7mm-08. Its based on the .308 hull just like the .243 only its just necked down to 7mm (.284cal) instead of 24 caliber like the .243. Compared to the .308 it kicks less and shoots flatter. Compared to the .243 it kicks a bit more (not much though) but gives you the ability to fire a 140gr bullet. I think the .243's heaviest bullet tops out at about 100grs or just a pinch higher. Almost any of the 140gr bullets would be fine for Mule Deer and a good premium bullet in 140 grain would be fine for Elk. I have one in a Browning A-bolt and my wife has no problem shooting it. With a good recoil pad I think your wife would actually enjoy shooting it unless she's very recoil sensitive.

Look up some ballistics for it online and for a low recoiling caliber I think you will be surprized at how flat it shoots.