I added a source to show that Anna (White) Nichols was married to James, not Jeremiah, Nichols. She is almost certainly the mother of the other Dorcas Nichols (Nicols) and at least five other children. She may have been born much earlier than 1713 if this is her birth record:
"Massachusetts Births and Christenings, 1639-1915," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:FZK3-K32 : 10 February 2018), Annah White, 17 Sep 1699; citing ANDOVER,ESSEX,MASSACHUSETTS, ; FHL microfilm 0496897 IT 1-2.
Sorry I can't fine anything on Dorcas (Nichols) Mote (my fifth great-grandmother), but at least we can disconnect her from the wrong Nichols family and sort them out.
Where does the name Jeremiah come from for Dorcas (Nichols) Mote's father? Is that from Luke Smith Mote? Should we keep him as her father but remove Anna (White) Nichols, who should be married to James, not Jeremiah?