Per the Alvord genealogy, she married first, ___ Looman. According to an online database of uncertain validity, they were married about 1760, and had one child [2]:
Mindwell (White) (Looman) White died October 10, 1768 and was buried in Evergreen Cemetery, South Hadley, Massachusetts [3].
Sources
↑ "A Genealogy of the Descendants of Alexander Alvord", Compiled by Samuel Morgan Alvord, (published 1908 by A.D. Andrews, Printer, Webster, NY. By the Alford American Family Association); no. 60.b: https://archive.org/details/genealogyofdesce00alvo/page/62.
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DNA Connections
It may be possible to confirm family relationships with Mindwell by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Mindwell: