Linda,
My family are the Footes of Cayuga, Mississippi. The towns Cayuga and Utica, Mississippi were named by a former New York State resident by the name of Oziah Osborn.
My Footes are of the Virginia branch. I believe that Ambrose Foote would likely be a descendant of Nathaniel Foote of Conn. or of John Foote of NY. Many of these Footes ended up in Michigan.
Please see the book by Abram William Foote on Nathaniel Foote located at Google Books. There are several Ambrose Footes listed in this book. There is a later edition (expanded) to this book on Google Books also, so check both.
He also includes in his book short bits about other Foote families including, Richard Foote of Virginia (mine), John Foote of New York, Pasco Foote of Mass.
Plus there is another book by Nathaniel Goodwin at Google on the Nathaniel Foote family.
Both the Virginia Footes and the Conn. Footes originated in Cornwall, England and are likely related.
Also research indicates that my wife might be related to the Northern Foote. More research is required though.