Don't use two servers. If the server can't cope, get a better server.
Umm, sorry but pretty much every MMO out there runs on more than one server.
The trick is to program your server logic so it can be easily paralleled between nodes. Take a look at bigWorld for example, they can handle more than 100K concurrent users distributed over tons of server nodes.
From the start you should program your server so it can be easily expanded if need be. For example, in my MMO Renoria, the server works like this:
1. Central Server (Main command server, controls communication between all nodes and controls security and acts as a pipe between nodes)
2. Login Server (Authentication server, controls user login and transition into one of the game server nodes).
3. Game Server (Actual server where the game is played. Handles everything in game, from movement, to attacks, to trading, to banning etc)
4. Game Server Node (Node attached to the game server, to offload any potential work that may lag the game server itself. Any amount of these nodes can be started and stopped at any time without affecting the game itself. This is only to load balance the game server).
5. Database Server (This server controls all the database transactions, and I use a MySQL cluster in Renoria).
6. Admin server (Server controls connections to RMT (Management tool) and the iOS/Android app used as a remote control for the server. Will provide constant updates to server load, player capacity, etc).
7. Cheat/Security server (This server logs all the cheating entries and broadcasts warnings about possible cheaters to the game masters. Will send constant updates on cheating thresholds attached to players).
All these servers register with the central server and once registered through the central server they may communicate with any other node by sending a request to the central server.