There are five different versions of the Kaddish. Chatzi Kaddish, Kaddish Shalem, Kaddish Titkabeil, Kaddish Yatom, Kaddish D'Rabbanan, and Kaddish L'itchadatah. Chatzi Kaddish separates between sections of a worship service. Kaddish Shaleim is recited at the end of a worship service; this is in addition to the Kaddish Yatom or Mourner's Kaddish. Kaddish D'Rabbanan is the "scholar's Kaddish" and is recited upon the completion of study. Lastly, the Kaddish L'itchdatah is an expanded form of the Mourner's Kaddish recited by some at the cemetery after a burial. It is this final version, Kaddish L'itchadatah, that is found in the UPB and includes additional Aramaic text that you have asked about in your post to iWorship [the extra paragraph in Mourner's Kaddish in the Union Prayer Book]. Interestingly, this additional text was most often eliminated on the pulpit by rabbis during the heyday of UPB use in Reform Temples; this was my experience in the Detroit metropolitan area during my formative years!
The UPB service is heard regularly on WQXR in New York (96.3 FM) on Fridays from 5:30-6:00pm. WQXR has a live-streaming aspect on its website, www.wqxr.com. For those who do not live in New York area, you may be able to access the service remotely in this way.
Cantor Alane Katzew Director of Music Programming URJ Department of Worship, Music and Religious Living