your axle is plenty strong enough to carry your rig.
I think only one lug nut was on, and it got loose and broke.
look at the other studs for wear/rounding near the axle plate.
if the threads are worn down, that happened just before the wheel came off.
replace the stud, fix the brake parts, and tighten the lug nuts to 80 ft/lbs or what the manufacturer recommends.