This is the first issue to consider when (thinking about) implementing a clustered server configuration. I'm surprised that you have only realized it after the fact.
Regardless of the data structure you store in the Session state bag, your problem will remain the same. The problem is not in the Dataset, but in the Session which is being stored with the ASP.NET worker process. You should look into the other options of state storage, especially State Server or SQL Server. In both cases, state is always retrieved from a common designated location/drive.
