That just can't be. SSRs are optically isolated, the load end shouldn't give a hoot where its power is coming from.
Really man, I don't want to be off on a tangent here without all the information. I'm trying to be helpful. I am not assuming that you don't have the proper equipment, or that you don't have this all figured out, but it would help to know specific values on your resistive loads, your inductive loads, your PWM and sensors, etc. If you told me you were using a 100 K resistor and it still flickers, I'd forget about the whole power supply thing. Otherwise I can't help but wonder about your supply.
I used many different things. A few Led's, a tester, a roughly 1 amp inductor etc.
I'm telling you if both ends of the relay are connected to the same battery the led on the relay goes off. If you take away one wire on the load end it goes back on. Driving me nuts cause it makes no sense.