I know it is counter intuitive but if your pressure goes up with the skimmer only, it means that there is less restriction via the skimmer and not more. Pressure is measured on the return side not the suction so it reads as the opposite for the suction side.

It is typical in a pool to have the main drain have more restriction than the skimmer since it is a longer run and usually smaller pipe so you may be ok there. Before you cut any pipe, I would make sure you acutally have a problem. From what you have said, everything sounds normal to me.

You will not get the PSI down to 12 unless you change your pump to a lower HP. Larger HP means higher PSI. I hyave a 1 HP motor and my pressure is about 20 PSI so I think this is probably normal for you.

Also, it sounds as though you may be cleaning something out of the pool since it raises from 20 PSI to 30 PSI in a short period of time.