Re: 243 win hunting bullet????
It is quite possible that the 1-9.5 will stabilize your VLDs, although I may caution you on it. A bullet that is known to be frangible when used on (intended) deer sized game, very well not make it into the vitals of an elk (predictably), the 243 is really light for elk, make sure you coach your daughter on proper bullet placement & keep the range short. Can it be done? Absolutely, has been many, many times over, but your chances for failure are fairly high as well. You might research the 85grn TSX, It will penetrate farther than the VLD which should be beneficial in this case, it will also hold together much better in the event bone is contacted.
Over penetration/expansion issues on your muley should not be an issue either, as I believe deer was the intended recipient for the 6mm 85grn TSX.