There currently is not a built in way to switch between types of date filters. I recommend voting on https://community.tableau.com/ideas/2159
The Tableau website has an Ideas section where customers can add, comment, and vote on features they would like to see in the product. Votes are used to help prioritize new features. Our Development team also loves to see everyone's use cases in the comments, which helps them better design features that will meet the most possible needs.
The attached workbook uses three parameters to get similar functionality (directions in workbook), but the parameter controls will not look like the range of date card or the relative date card.
Hope this answers your question