When you create a dataset, you get the option of including the database file in your project, instead of the connection string pointing to the database file in the sql server data folder. My question is, is you select no, how can you later, after creating the dataset, change your mind and change, that the database file should be included in your project, and should be included in the release folder
You can use the same option as you would to include any other existing item in your project.
You can then change the connection string in the Settings for the project, but I'm not sure whether that will work at design time or only run time. You can easily enough just delete the DataSet and regenerate the Data Source.
The data file will be included in the output folder by default, but you should change the Copy to Output Directory property to Copy If Newer unless you want to lose any changes you made during testing each time you build.