Depending on how deep you want an explanation and how capable you are of setting up your Server and Network, a dual NAT/PAT situation can be very safe, but hard to manage. especially if your setup runs for a long time, and suddenly something changes/breaks. Then you are most likely up to a longer debugging session. But that is no reason for not doing it ;)
So as @lungj already wrote, a second internal LAN would be very safe. Especially If your Minecraft server would really be compromised, you could easily deny any communication out of that Subnet.
The question is, if you relay need a second router for that of if you current router is already capable of handling multiple subnet, and firewalling the communication between those. This would also reduce the complexity level a lot.
+~~~~~~~~~~~~~~+
( Internet )
) (
+~~~~~+^~~~~~~~+
||
||
||
+-----v+-------+
| Router1 |
| |
+-----+^-------+
||
||
+-----||------------------------------+ +----------------------------------------+
| ||LAN segment 1 (private) | | LAN segment 2 (DMZ) |
|-----||------------------------------| |----------------------------------------|
| || | | |
| || | | |
| || +--------------+ | | +--------------+ |
| |+-------------+ Router2 +------------------------> MinecraftSRV | |
| +^-------------> | | | | | |
| || +--------------+ | | +--------------+ |
|+----v+-----------+ | | |
|| other Hosts...| | | |
|| | | | |
|+-----------------+ | | |
+-------------------------------------+ +----------------------------------------+
Here is a little diagram of the proposed (complex) sollution.
If Router 1 could have second IP on another interface, and good Firewall, the same setup could be achieved without a 2nd Router in your private LAN.
If you'l set it up with a second router, dont forget to add a static route on Router1 into the DMZ over Router2 in order to communicate inwards into the LAN segment!