Electro magnetic interferences (EMI) generated by power circuit reset low voltage integrated circuits (ICs)

The main question here is (explanation will follow):
Is there a way to filter out low voltage oscillations (>10MHz) on pins that have to stay high for the system to function? Oscillations are induced by EMI emitted by power circuit during relay bouncing). RC filters 100Ohm/100nF did not work. Traces are ~50cm long.

[Explanation]:

I’m currently struggling with proper EMI filtering for the low voltage control circuit that is responsible for switching on/off high voltage capacitors using relays.

I realize that the low level part of the circuit has a bunch of design flaws (e.g. the logic signal between uC and shift-reg could’ve been arranged into a differential pair). But currently I’m trying to figure out a way to modify the circuit with as little PCB modifications as possible.

Here is the essential part of the setup:

Power circuit is operating on fairly high voltage and current, but I don’t care about the quality of power of this circuit, moreover I cannot modify it.

The only issue I have to deal with looks like this (the description will follow):

• Yellow – Power circuit voltage
• Blue – Power circuit current
• Green – logic signal (EN or CLR, see schematics)

Green signal represents EN or CLR; it is a CMOS 3.3V open-drain pin. When voltage falls below certain treshold (I guess 1.8V) it is no longer high, therefore the shift-reg resets. It cannot reset.