I also had a problem sharing a DVD file on my FCP version 10.2.3 and Mac OS 10.11.4. I was creating many different DVD video .img files stored on hard disk, but ran into a problem with one share locking up at 66% completion. I found other threads that discussed a 66% lockup problem while creating DVDs. One solution (also given in this thread) was to try adding then removing a background graphic. Note that I was not providing a background graphic in any of the DVD files I was creating, so it was weird that I was getting a lockup on the problem DVD share. Anyway, I tried the add, then removal of a background graphic (.jpg). Unfortunately this did not work for me. What did work was to actually add the graphic and leave it in. Then the DVD file was successfully created and I haven't had a problem with DVD sharing since.
Btw, I did find the following Apple notice that talks about a similar issue.
Final Cut Pro X, Motion 5: Share to DVD returns alert "The operation couldn't be completed. (DSPPublishing error -29)" -…
Good luck!