You're talking about 2 different things:
- Exporting a module
- Creating an install package for a module
Exporting a module, will not export the module class definitions with it. Whereas creating an install package will.
That all being said, if you go to export the module you can include the tables. To do so, go to Sites > Export > Next > Expand Development and select Modules. Next select the module you want to export. Then click System tables and check the tables which are part of your module you want to export.
This should get you what you're looking for. The larger problem is you can't "reinstall" a module in another environment if it's already been installed. So I suggest you fine tune the module and all the classes before you import it into another environment.