Triac fails unusually
For one, I'm surprised that this circuit functions at all, even with one triac in place. The power triacs (BT136-600D) connections should be flipped, with the AC hot wire connected to MT2 and the AC neutral wire connected to MT1 as can be seen in the datasheet.



Triacs are thought of as completely symmetrical devices but in reality their slight asymmetry makes them not function correctly when the terminals are flipped. This could possibly be the solution to your problem. Additionally, depending on what other components you have hooked up to your microcontroller, it is possible that you are attempting to draw to much current from it. The datasheet for the MOC3041M says that the max current draw of the phototriac is 15 mA, this can easily be supplied by a single pin of most microcontrollers but there is still a maximum total for the MCU which could be exceeded by adding an additional MOC3041M.