I have a 200 amp main panel and would like to know what wire size do I need for a 125 amp sub panel that's about 55' feet away from the main panel.The 125 amp sub panel is going to be used for a in-law unit in the back yard.The unit is about 400 sq ft, a small room, living room, bathroom, kitchen with a small 24" electric stove and refrigerator.Also the sub panel in the main house is a 100 amp, did I screw up by buying the 125 amp sub panel for the in-law unit. I bought the murray brand because it had more spaces.The last 20' ft is under ground what p.v.c size do I use.

Using NEC table 310.15 (B)(6) Special Ampacity rating for service and feeder cables you need a 2/3 feeder cable. It must be a four conductor run to the panel at the in-law residence.

Because you have a Main Panel and an Existing Sub panel and a new planned 125 amp subpanel, I strongly urge you to get a load calculation assessment completed, by a licensed electrician and to make sure you have the required electrical permits in place.

This study will also make sure that you are within the capacity of your 200 Amp service.

I also urge you to consider using the services of a licensed electrician to run the feeder and make sure that the wiring of the new sub panel is up to code.

The size of the sub panel does not matter. You limit the service going to it with the breaker in the main panel. In other words you have a 125 sub panel but you limit the service with a 60 amp breaker in the main panel. The main breaker in the sub panel then becomes only a disconnect switch. The size of the breaker in the main panel is determined by the size wire used. Wire size determined by the calculated load.