Double Shielding -- Insulator between shields?
You want to make sure that no currents from your device can inadvertently run thru a shield.  That means there can be at most one connection back to the device or the next-inner shield.

For capacitive shielding, you want the shields connected to the ground of the device.

To satisfy both these constraints, connect the inner shield to the ground of your device in exactly one point.  Then connect the outer shield to the inner shield at the same point.  That way the inner shield still has only one connection.

Just two shields might not do what you want.  Shields don't let RF waves thru.  However, they can act as antennas and receive radiation from one side.  This antenna then re-radiates some portion of the received power to both side.  This in practice makes shields not block all radiation.

You might consider absorbing material between the two shields.  There are ferrite tiles and various carbon-impregnated foams for this purpose.  You have to check the frequency range and absorption characteristics of any such material carefully.

It would probably be useful to have a chat with a application engineer from a company that makes RF-absorbing material.