Wirelessly posted (BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

Unless there is a Business Class on this route that is clearly superior to AA's, I would use the BA miles to fly AA. Your in-laws would get to use the Admirals Club at both ends, and AA's J seat on the three-class transcon is comfortable. Moreover, you would not have to pay any fuel surcharges when redeeming BA miles on this route.

Since BA permits en-route stopovers on award redemptions, you could probably add on a Coach leg -- to be flown at a later date -- from LAX to places like SFO, LAS, RNO, PHX, etc., as long as BA approved the award routing.