Design considerations for creating an Arduino 'shield' shield to limit EMI
What would be helpful would be explanation of the type of AC you are using and then possibly a schematic or board layout.

That aside, there does seem to be noise between the two boards. The Idea of placing a PCB with just a large copper pour would work. 

DC Ground 

If you connect the DC ground from the main board you should use a ferrite bead(FB) between the two grounds, this will ensure that you don't get noise getting back into the ground of the main board after you have tried to shield it. You should try to match the ferrite bead to the noise frequency you experiencing (use a scope if you have one).

Using the DC ground as a shield is often done, if you look at the EMI cages on cellular phones, WiFi modules, and other noise generating devices/susceptible-to-noise devices, they are connected to ground. It gives the noise somewhere to go, instead of your signal lines. Thus using the DC ground is defiantly an option

i.e.:

Main ground&gt;--------[__FB__]-------&lt;SHIELD


AC Ground 

You could use the AC earth line on the top part of the shielding board. The coupling part might be a bit over kill, leave space for it to test to see if it helps when you make the board. Also AC earth can be used for shielding but is used for the safety aspect of earth leakage.

Don't do a direct DC ground to AC ground unless you know what you are doing as this will create a ground loop, this will change the way stuff behaves and will make your circuit no longer a floating device.

Other stuff 

I would also make sure how you drive the relay is isolated from the control circuitry, although from what you describe:


  if I move the shield further away I also don't see the issues.


If you share power rails between the relay board and the main board, try filtering the power going to the CPU section. Also the control lines can be isolated between the controller and the relay with opto-couplers, this might stop noise coming back into the circuit from the relay part.