As for the Book of Abraham upon which this doctrine is, in part, based, it was proven to have absolutely nothing to do with Abraham, but rather was an Egyptian "Book of Breathings" back in the 1960's. The evidence on this point is so well-known and so conclusive that I personally find it surprising that there are still Mormon apologists trying to defend this document.
Here are a couple of the many sites
where one can see the history behind the scroll which Joseph Smith claimed
contained the "Book of Abraham".
A quote from the last document:
One Nation Under Gods
An excellent resource book for those who wish to gain a good insight into the history or the Mormon Church. Highly Recommended.
Click here for a short (6+ minutes) video which briefly goes through some of the key problems with the Book of Abraham.
For those who want to look into this further, we have a link under additional resources where a more detailed video regarding the Book of Abraham may be purchased.
Translation of the "Book of Abraham" Scroll in 2003
In addition, in 2003 Robert K. Ritner, Professor of Egyptology at the University of Chicago produced an updated translated of the scroll in the Journal of Near Eastern Studies, Vol. 62, No. 3 (2003). The article is titled, THE BREATHING PERMIT OF HÔR” AMONG THE JOSEPH SMITH PAPYRII.
Details can be obtained by clicking on the links above or here:
Resume of Robert K. Ritner: Robert K. Ritner, Professor of Egyptology
Probably one of the best detailed resources on this controversy is the book, By His Own Hand Upon Papyrus, by Charles Larson, available both on-line or can be purchased (see information on obtaining a copy of the book below). For those who want to see a brief summary of the conclusions and findings of the book, here is a link to the final section:
By His Own Hand Upon Papyrus
This is the story of the Book of Abraham from start to finish. Highly recommended for those who want the detailed history and facts surrounding this book and the players involved in the controversy. The book may also be read on-line:
Reasoning from the Scriptures with Mormons
Also, check out the videos available from Living Hope Ministries, especially the DNA vs The Book of Mormon Video. This is one of the most important videos in the history of Mormonism and shows absolute proof that the book of Mormon is false. Living Hope Ministries makes this video available on-line, as well as in tapes which are free to Mormons or available at very low cost to those who wish to make this important information available to Mormons.
Details and background information regarding those involved in the DNA movie may be found here.
The Lost Book of Abraham Video
This is another video available for purchase from Living Hope Ministries which explains the problems with the Book of Abraham, a book which the Mormon Church claims to be an important piece of their scripture.
Additional information regarding the video is found here.