The workspace (rm2db) file will contain track information, including position and depth required for making bathymetric maps. Copying this file back and forth is all that is required to keep map projects in sync if all they contain is generated components (isobaths, contours etc).
If you want to view sonar logs or use sidescan mosaic, then the original sonar log files are required, and these must be in the same relative disk position on both computers - e.g. if you store sonar logs in C:\Sonar Logs on one machine, then this should be replicated on the other and the files within each should be kept in sync. The same applies for any image (.mbtiles) files that are used as backgrounds or as map image layers.