I have tried understanding your requirement. Based what I think, you have asked, here is a tentative solution.
Try to have the data in this format :
Even, if you have Start Date and End Date as columns, in the "Edit Data Source" page, pivot the data, so that you get this format.
Now, in your viz, when you drop "Dates" in columns, Tableau would automatically add the between dates.
Hope this helps.
If it answers your question, please mark it as the "Correct Answer" for others to help.