I worked on a data dashboard site that embedded Tableau workbooks. I found their JS API to be decent for embedding workbooks[0]. I used what Tableau calls "Trusted Authentication" to handle the authentication to Tableau Server[1]. It's harder if they are using Tableau Online.

[0] https://onlinehelp.tableau.com/current/api/js_api/en-us/Java... [1] https://onlinehelp.tableau.com/current/server/en-us/trusted_...