Dimmer on Due: digitalWrite on one pin affects digital value of another
There are a few issues with your circuit.  

First, you need to add a diode to your 4N25 circuit.  See EDIT below.     You should still put a diode across your 4N25 LED.  Right now, your 4N25 diode (LED) gets a high voltage across it 1/2 of the time.  Because you have 60K (30K+30K) in the circuit, the LED is likely not damaged, however the LED isn't really designed to handle reverse voltage more than 6 volts. Depending upon the reverse characteristics of the Bridge diodes (leakage current), your 4N25 LED could be experiencing greater than 6 volts.  Using devices beyond their "maximum specification" can produce unusual side effects. 

Place the new diode (1N4007 is good, almost any diode will work) across the LED on your 4N25. Wire the new diode with new diode anode to the LEd cathode. Now, the LED will turn on during 1/2 cycle of the AC,  and be protected against overvoltage during the other half of the cycle.  

Second,  rearrange your circuit for the Triac.  The data sheet for your MOC3043 triac driver shows a typical schematic.  



Notice the 39 ohm resistor and the 0.01 uf capacitor in the circuit.  This is called a snubber and will reduce interference and voltage spikes. This type of interference is famous for disrupting low voltage circuits such as micro-controllers.  

Without seeing your code, I can't say much on that.  However, I presume that you are trying to detect the zero cross, and then waiting a certain amount of time AFTER the zero cross to turn on the Triac.   


  I measured current on the controlPin, it's only 3.2mA   


Your 3.2mA may not be enough to drive the LED in your dimmer circuit. You will likely need 10mA to assure proper operation.  You can reduce the resistor to achieve higher current to the MOC3043.   

EDIT  :  I just realized that your bridge rectifier protects the LED (4N25) from reverse voltage.