"From what I interpreted, I can only claim losses on the sale after the date of death. . . ."
As Rick19744 said, there is no gain or loss until you actually sell the stock. Changes in market value are only "paper" or "unrealized" gain or loss. They have no effect on your tax. When you sell the stock, your gain or loss is simply the difference between what you sell it for and your basis, which is usually the fair market value (FMV) on the date of your mother's death. It has nothing to do with any previous market fluctuations.
If you transfer shares of stock "in kind" to your siblings, there are no income tax considerations, but you might have to file gift tax returns (Form 709). If you sell the stock and give your siblings cash, then you have to report the sale on your own income tax return, and you might have a gain or a loss. The gift tax considerations also still apply to the cash gifts, based on the dollar amounts. You cannot file a gift tax return with TurboTax.
Just a bit of semantics: Everybody uses the term "stepped up basis," but your basis is the FMV on the date of your mother's death (or on the alternate valuation date). It could be stepped up or stepped down, depending on what your mother paid for the stock.
