dmacl...The 7mm-08 is a .308 case necked down to a 7mm or .284..
Came out in 1980 if I remember correctly, it had been a wildcat for several years, until Remington made it a factory loading...My brother has had one since 1982 or so...The most popular bullet weight is 140grs, and most factory loadings are 2850fps or so...The 7mm-08 would be a good choice...

But, depending on how often you go elk hunting the 30-06 is better....Just use reduced recoil loadings for your wife and daughter...Use 150 or 165 gr bullets for deer and antelope and 180 grs for elk...I believe it was Jack O'Connor that said he preferred a .270 for hunters going after deer sized game and smaller and a 30-06 for hunters going after deer sized game and larger...