> However, in some records, I keep coming across an
> "Elizabeth Vincent."

I have never seen a record of that nature. Don't you mean "online accounts" rather than "records?"

> as I learned "Mary" and "Elizabeth" were often
> interchangeable during the time period

I suggest that you consider the place where you heard that as unreliable, because those names were not interchangable.

> nothing supports this in the online research I've done

That is perhaps the crux of your problems - some of the most reliable resources for genealogical research are often not available online, and if they are online are sometimes available only on subscription-only sites such as Ancestry.com or member-only sites such as AmericanAncestors.com. Those reliable resources include the major scholarly genealogical journals, transcribed or abstracted contemporary records, and, best of all, images of contemporary records taken from Family History Library microfilm. The last of those (a collection which is always growing) are at FamilySearch.org, although navigating the images to find a particular record is sometimes a bit difficult.

Sarah Allerton's marriage to John Vincent has been noted in print since at least about 1900. A reliable reference to that marriage was published in 1905 [Mayflower Descendant, 7 (1905):129-130] - the Leyden record of her marriage to Degory Priest calls her "widow of John Vincent."

The short answer to your original question is that I have seen no contemporary record establishing a daughter for John and Sarah (Allerton) Vincent.

Dale H. Cook, Member, NEHGS and MA Society of Mayflower Descendants;
Plymouth Co. MA Coordinator for the USGenWeb Project
Administrator of http://plymouthcolony.net