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This is not a wheel balance problem. The reason why the wheel shakes is because the rotors are overheating. This causes them to warp and translates into a steering wheel vibration. You have one of two possible things going on here, the brake calipers are both hanging up at the same time which is unlikely or the most common problem is the pressure is not being relieved back into the master cylinder due to the valve sticking in the master cylinder. t Ts eventually causes the pressure to build then as the calipers and brake pads get hotter and hotter it causes them to even sees onto the rotors even more. The easiest way to determine if this is the problem is to have the front wheels off the ground while the calipers are bound up and the wheels are difficult to turn then crack the line loose at the master cylinder and see if the pressure releases and the wheels turn freely. If it does then you know for certain the problem is in the master cylinder.

Sorry for the delay. I had to step out for a while. If the brake pads need to be replaced because they're worn out and hanging up in the brake pad holder then yes this should take care the problem. However if it is a pressure buildup due to a bad valve in the master cylinder then no it will continue to become a problem. The master cylinder needs to be inspected when the brakes are done.