Hi Ante,
Your full-wave rectifier circuit works fine at low frequencies, I have used it many times. Its "full-wave" becomes assymetrical above about 2KHz, unless you use a wide bandwidth opamp like a TL074, which rectifies well up to about 25KHz in this circuit.
The TL074 has FET inputs so RV2 is unecessary (input pin 10 connects directly to ground), but an offset voltage adjustment is needed with any opamp for very low-level inputs.