Prior ArcObjects release ver 10.0 there was an ISchematicExport interface who has methods to programmatically implement ArcSchematic Dataset export to another GeoDatabase.
From ArcObjects 10.0 and later this interface is not available any more. There is no Schematic GP Tool for such task as well.
Would be very helpful to return this functionality to ArcObjects. Another option - create new GP Tool that could export Schematic Dataset with the same functionality as ArcCatalog tool "Export Schematic Dataset to Geodatabase".