I have been dealing with Galtmaster taps for weeks now. I finally have been able to remove the taps, replace the packing and washers and the valve seats. I now have taps that don't leak! That was only part of the problem though. I also have a diverter valve that is broken. Meaning that the shaft simply spins and cannot be used to remove the valve. I have removed the outer nut, but the valve itself usually is removed by turning the shaft of the valve. Any ideas on how I can remove the diverter? If anyone wants help with how I removed the taps, just let me know.

Not familiar with that brand. Can you show pic? Usually the first nut around a stem is the packing nut. It prevents leaking around the stem. The second nut would be the shoulders of the stem body and used to remove the stem. Show pic.