Should the ground plane of a noisy mezzanine card be connected to the ground plane of the main card by metal mounting hardware?
Given the information provided it is very difficult to give anything but general advice.


Understand what the source is. Try to reduce the amplitude at the
source. 
Understand what the antenna is. Try to make the antenna
less efficient. 
Shield the whole thing.


My experience with getting multi-board systems through EMI testing is that it is so much hassle than I always opt for a metal enclosure around any multi-board system. Use the metal enclosure as a Faraday cage and make sure everything passing though the enclosure is sufficiently filtered to the enclosure. And avoid having the enclosure itself be the (return) path for any high frequency signals.

My experience with single-board systems is that they can usually go through EMI testing with some basic care. Especially around power supply (PDN design - I use PDNTool.com to make a low impedance bypass across the whole frequency range) and filtering for connectors. Consider placing all connections along one edge.

Maybe these answers can help you as well:


EMC testing of unenclosed PCB assembly
Where to connect shield and ferrites in PCB with isolated planes
Grounding PCB to enclosure


(sorry for the non-exhaustive list, but I answered on these so they were quick to find for me and there is at least one coherent answer in those that follows my thinking :-)

In short: It sounds like you need a metal enclosure for the 2-board system you are building. But start by understanding. If it is too hard to understand what is going on - seek help. Two heads are better than one. Peer review is an underrated but very useful activity.