Home Air Conditioner Problem
The problem you describe is considered normal performance for many residential A/C units.  By design, these only function correctly if the outdoor temperature is warmer than mid 70s and the indoor temperature is above 68F.   Below these temperatures, the evaporator coil gets colder than freezing, becoming worse as the coil accumulates frost, eventually causing the system to become covered in ice and stop cooling until the unit is manually shut down and thawed.

In a situation such as yours where A/C needs to perform even during cool temperatures, it is necessary to install three accessories which will enable the unit to operate under these conditions:

(1)  A compressor crankcase heater (sized for your compressor)


(2)  A head pressure control (such as Totaline p251-0083h, approx $35 new, Ebay)

(3)  A evaporator control limit (ECL) switch or Freezestat (approx $20 new, Ebay)

Calibrating the head pressure control perfectly requires a set of gauges, but it usually works correctly if the temperature probe is placed anywhere near the discharge of the condenser coil.  Other than that, these are electrical items only, requiring no refrigerant expertise.  This setup is sometimes referred to as a "low ambient kit with freezestat."  An experienced tech should be able to install all these within a couple hours.