Two ways:
1. use the federated engine to enable one Mysql server to talk to the other;
2. have WordPress talk to both. Create a second wpdb object that talks to the non-WordPress database. This is quite possible, and you can give it non-WordPress-related queries. See Using wpdb to connect to a separate database for more.
The fly in the ointment is transactions. Actually, out-of-the-box WordPress doesn’t even do transactions at all. That’s a bigger issue with multiple servers. How to do that right would be good question by itself.