SMPS dipping periodically when wall voltage is under heavy load
First, that is a very nice schematic, especially coming from LTSpice. 

I don't see any reason for interaction between the motor and the power supply, except possibly because your mains voltage is dropping. 

However, presumably those LEDs illuminate at higher motor power so the current draw progressively increases with increasing motor speed and there is also the opto drive current. I would suggest testing the power supply at the full circuit current draw from the 12V (add 20% for margin) and input mains at nominal voltage less 20% and see if the output 12V remains in regulation. 

I don't know how much your pressure sensor draws, but you might be getting close to the maximum capability of the LNK302, even if you are using the recommended inductor etc. 

Edit: Here is a guide from Tektronix on safely making mains measurements with an oscilloscope. Using a grounded input oscilloscope with reference connected to the neutral can cause inaccurate readings and can damage the oscilloscope as some of the motor current will flow through the scope probe and circuit.