The only machine that is strong enough to undo wheel nuts, is an airgun. As you are not likely to have a compressor with you, you will have to carry on using a wheel brace.
get one of those extending wheelnut bars (draper and others make them) comes with two two sided sockets to fit the wheelnuts ,despite my best efforts i havent found a nut it cant undo.
Try this. There are lots of different impact wrenches out there, Snap On is a popular one too but the Sealy 19.2v is a good one for the price, Snap On is around £300. They can take off a wheel nut with ease and a charged battery will last a whole day in a car workshop.
Having tried one, I have to say the extending wheel nut wrenches are preferable. Most motor accessory shops sell them, but the discount shops like Lidl are generally cheaper.
as torque (the force exerted on the nut) is force multiplied by distance if you cant increase the force increase the distance, good quality wrench and a length of pipe will remove most nuts. just be prepared if the wrench is not good quality to slip/shear.
my snap on half inch drive knuckle bar is a good bit of kit, 2 feet long and can take loads of force on it
Not forgetting they are guaranteed for life Alan. Got one eggs hatly the same as yours and if that along with a top quality socket can't undo it then you have got a problem.