A .308 kicks significantly more than a 6.5 CM depending on the load. If you stay in the 160 range (15ish pounds of recoil) or lighter it is still more than full power 6.5 CM (11ish foot pounds). However, if you move up to the 180s (unnecessary) it can be quite stout in an unsuppressed/braked rifle.
Also, do not worry about energy. This provides no indication about how a given bullet will perform. Instead lean on minimum FPS for terminal performance. For example, Hornady ELDM and ELDX expand reliably down to 1800 FPS, whereas partitions, accubonds, and barnes all copper bullets typically need 2000-2200 fps impact velocity.
The .223, .243/6mm, .257, .264/6.5mm, .277, and .284 are all more than adequate on elk given the appropriate cartridge and bullets. No need to get anything bigger. Guys have already referred or linked to the threads on Rokslide where this fact has been proven ad nauseum.
If it were me and I was buying one gun for the 3 kiddos and the goal is for all to be able to shoot it well relatively quickly, the "cost" of entry is the lowest for the .223 in terms of recoil and practice. If you stick with heavy expanding bullets they will do well. If you're not comfortable with a cartridge this small, my next pick would be a 6 Creed. Granted there is better ammo availability for the .243, but over time that will change.