Simply Practicing your golf swing at various stages and monitoring all the components, will build stabilizing muscles in your back. It seems to me that the back of this machine should be strong enough to handle the outward force instead of being thrown around by it. So the machine should be stabilized, feet bolted to the ground, stationary post and strong stabilizing leg and back muscles on the back of the machine. When practicing always practice 'proud posture' and your back muscles will build swing after swing. Soon proud posture will be automatic as the muscles have built up enough in the upper and lower back that the spine is pulled back straight enough without consciously doing it.
+1 to lynn's comments, the true swing does not use muscular effort, getting stronger can help to control the motion better but the speed and thrust are not created by muscular effort and so one should not concern himself with building arm muscle for power in a true swing. In fact be very careful of any amount of stress being put on the deltoids and rotator cuffs, the tour is filled with guys who've gone through career stalling shoulder surgeries.
My friend who is a true hitter and has tremendous distance, attributes all his power to this one exercise he has done thousands of times. It's a straight right arm extension with a cable pulley machine, with a turning body like the straight right in boxing only with both feet shoulder width apart and facing forward this builds his tricep muscles and stabilizing right shoulder muscles while stabilizing the core as well.