I don't know whether you have pressed in studs (American style) or threaded in studs as I have on my hubs, but it sounds like you have a press-in stud that has become stripped in the hole - that's why it's spinning in either direction but not coming out.
You're not going to be able to pull the stud out because it is flanged on the inside of the hub.
So, remove the other four nuts, then put the bad nut at the bottom (6 o'clock) position and, while pulling the top (12 o'clock) of the wheel towards you to use as a lever to hold the stud fast against the hub, use an impact wrench to spin the lug nut off. A bat handle won't do this, it must be an impact wrench (set on "high) and you'll need to apply lots of torque to the wheel as a lever to crimp the stud fast against the hub to hold it.
The only other alternative I can think of is to remove the center cap from the wheel and you should be able to get some needle-nose pliers in there to remove the cotter pin from the hub nut, then use a 36mm socket on an impact wrench (with e-brake applied hard) to remove the hub. You'll need to remove the caliper or caliper mount (with caliper attached ) to allow the hub to be removed with the wheel still attached. Then use an angle grinder to gently remove the stud head enough to let the stud pull through the hub flange. You may be able to get some heavy duty vice grips on the stud flange to hold it so an impact wrench can remove the nut, but that's a long shot.