Here's an image from a Church website that depicts the stone-in-a-hat scenario.
Look at this misleading statement (which is also in the Gospel Topics Essay) found in that web page:
"Joseph and his scribes wrote of two instruments used in translating the Book of Mormon."
This is misleading because Joseph never wrote of "two instruments." Nor did Oliver Cowdery.
In 1870, Martin Harris related an anecdote that claimed Joseph used both the Urim and Thummim and a seer stone, but he was referring to the dictation of the 116 pages, not today's Book of Mormon.
The only "scribe" who possibly wrote about "two instruments used in translating the Book of Mormon" was Emma Smith, and both accounts are problematic.
In 1870, Emma Smith wrote a letter to the wife of the RLDS pastor in Independence, Missouri, who had apparently asked about the translation. Emma wrote, "Now the first that my <husband> translated, was translated by the use of the Urim and Thummim, and that was the part that Martin Harris lost, after that he used a small stone, not exactly black, but was rather a dark color, I can not tell whether that account in the Times and Seasons is correct or not because some one stole <all> my books and I have none to refer to at present, if I can find one that has that account I will tell you what is true and what is not."
This statement is significant because it demonstrates that, as of 1870, the term "Urim and Thummim" was not used to refer to both the Nephite interpreters and the seer stone. Modern Church historians have invented a new definition of the term "Urim and Thummim" to include both the Nephite interpreters and the seer or "peep" stone Joseph found in a well, but that definition makes Emma's statement nonsense.
The statement is also significant because it is a direct contradiction of what Joseph and Oliver always taught, as well as Lucy Mack Smith's 1844-5 history. It also contradicts Martin's anecdote.
It is especially interesting that Emma could not remember the account published in the Times and Seasons (which published both Oliver Cowdery's Letter I and the History of Joseph Smith which is today's Joseph Smith--History in the Pearl of Great Price). We will never know whether she would have "remembered" things differently by referring to that account, but it's not a good sign when a witness forgets a more recent event (publication in the Times and Seasons) while claiming to remember an earlier event (the translation). Plus, her statement is ambiguous; she doesn't actually say Joseph translated today's Book of Mormon using the small stone.
By 1870, the issue had already become part of the controversy between the Utah Mormons (who accepted Brigham Young as prophet) and the other groups who claimed to be the rightful successors to Joseph Smith. Brigham Young and other members of the Quorum of the Twelve often reaffirmed Joseph's testimony that he translated the plates with the Urim and Thummim. Others claimed Joseph did not use the Urim and Thummim, but used a seer stone instead. This post is too short to get into the reasons, but the details are discussed in the new book, A Man that Can Translate.
In October 1879, a statement attributed to Emma was published the month after Orson Pratt gave two sermons in which he reaffirmed that Joseph translated the Book of Mormon by using the Urim and Thummim. Emma's alleged "Last Testimony" claimed Emma wrote while Joseph dictated with his face "buried in his hat, with the stone in it" but does not specify what part, if any, of today's Book of Mormon he dictated this way. Emma did not write this statement; her son, Joseph Smith III, President of the RLDS Church, published it as an interview several months after she died.
Contrary to the statement in the web page quoted above, neither Joseph nor any of his scribes wrote of two instruments used to translate the Book of Mormon.
Joseph and Oliver repeatedly testified Joseph used the Urim and Thummim. They never wrote or said anything about a second instrument.
Martin said nothing about the translation of the Book of Mormon we have today.
Emma's letter claimed Joseph did not use the Urim and Thummim after the 116 pages were lost, but she admitted she needed a copy of the Times and Seasons to tell what was true and what was not.
Emma's "Last Testimony" claims Joseph dictated with his face buried in a hat with a stone in it, but does not specify what parts, if any, of today's Book of Mormon he dictated this way.
The only unambiguous explanation for the translation of the Book of Mormon is the one Joseph and Oliver always gave. They said Joseph translated the engravings on the plates by using the Urim and Thummim that came with the plates.
For me, the testimonies of Joseph and Oliver outweigh all the other statements by observers, but others are free to interpret the evidence however they see fit.
However, is it too much to ask to have accurate statements on the Church's website instead of misleading ones such as the one quoted above?
Here's the official account from the Pearl of Great Price. Note that none of these passages are quoted in the above website on the translation. Note also that the messenger referred to the stones in silver bows as the Urim and Thummim.
34 He said there was a book deposited, written upon gold plates, giving an account of the former inhabitants of this continent, and the source from whence they sprang. He also said that the fulness of the everlasting Gospel was contained in it, as delivered by the Savior to the ancient inhabitants;
35 Also, that there were two stones in silver bows—and these stones, fastened to a breastplate, constituted what is called the Urim and Thummim—deposited with the plates; and the possession and use of these stones were what constituted “seers” in ancient or former times; and that God had prepared them for the purpose of translating the book.
42 Again, he told me, that when I got those plates of which he had spoken—for the time that they should be obtained was not yet fulfilled—I should not show them to any person; neither the breastplate with the Urim and Thummim; only to those to whom I should be commanded to show them; if I did I should be destroyed.
52 Having removed the earth, I obtained a lever, which I got fixed under the edge of the stone, and with a little exertion raised it up. I looked in, and there indeed did I behold the plates, the Urim and Thummim, and the breastplate, as stated by the messenger.
Maybe someday soon we'll have the statements attributed to Emma Smith and Martin Harris and David Whitmer canonized. We shouldn't be surprised, I suppose. But until then, I stick with what Joseph and Oliver said.