microcontroller - Grounding the chassis with capacitor

My question involves chassis grounding to earth ground.

My PCB circuit is a simple signal generator using a microcontroller. It has a separate 'ground' from earth ground, supplied by a floating 5VDC source. (I guess we would call this a digital ground?)

The PCB is to be installed inside a metal chassis (aluminum, I believe). Inside, there is a 15VDC converter. As a signal generator, it outputs a signal with reference to the +5V.

Unfortunately, the device that uses this output signal is grounded to the earth ground, not the digital ground.

The signal, which is supposed to drive a motor, ends up having severe noise problems.

What I found out was that if I provide the chassis (not the circuit ground) a capacitative ground to the earth ground by connecting a capacitor from the chassis to the earth ground pin, the noise problem disappears. However, if I connect the earth ground DIRECTLY to the chassis, the circuit is shorted.

So my question would be, is it normal/safe to ground the chassis of a circuit with digital ground using only a capacitor? If not, is there a better way to fix the noise issue?

Also, even with the capacitor to the earth ground, whenever a large machinery sharing the same earth ground turns on, my device shorts for an instant, and resets the microcontroller. Is this caused by a large current draw from the big machinery? But how so, if only the earth ground is common?

Answer

After some experimentation, I found out that it is indeed okay to have capacitative coupling between chassis and earth ground. In the question, I wrote,

if I connect the earth ground DIRECTLY to the chassis, the circuit is shorted.

This is not true, and it was actually caused by me shorting the 5V supply accidentally.

There were several problems at hand. First, my DC voltage supply was isolated and floating off some weird value. This meant that the 'negative' of the supply wasn't actually connected to the earth ground. As stated in the question, I wanted to drive a motor that was connected to earth ground. Fortunately, the motor only required a differential voltage, hence it functioned okay.

Another issue was the microcontroller resetting whenever a large machinery turned on. This was solved by putting bypass capacitors between all VCC and GND connections (even for the LCD screen that I have as well). Thanks to @Horta for the suggestion! Although, it still is a mystery to me why there was voltage fluctuation within the earth ground in the first place.

Thank you everyone for your help!