Brian C. Hales concludes that the story of Emma Smith pushing Eliza Snow down the stairs is likely "folklore."
Brian C. Hales, "Emma Smith, Eliza R. Snow, and the Reported Incident on the Stairs," Mormon Historical Studies 10, no. 2 (Fall 2009): 73
In summary, multiple problems with the accounts and their claims can be identified. The narratives all appear to have undergone at least one retelling, if not several, over the span of many years. The proposed chronology is also problematic because Emma likely knew of Eliza’s sealing to Joseph before the Smith family’s move into the Mansion House and consequently would not have been inclined to permit Eliza to live there afterwards. Less plausible is the description of Joseph kissing or embracing Eliza in Emma’s plain view. Other inconsistencies are noted respecting the portrayal of the structure of the staircase, as well as issues of pregnancy, miscarriage, and possible posttraumatic sterility.
. . . .A review of available manuscript documents leads to the conclusion that folklore predominates where historical evidence is unavailable.