You have confused things by trying to make these two different families/individuals. (Hugh born about 1727 with a son Hugh born about 1748 and James Hugh born 1730 with a son Hugh/Huey born 1758.)
There are no known records in the United States of a person in the 1700s of the name of James Hugh BAY. Please cite one original record showing the existence of such a person.There are none.His name was simply Hugh BAY.He was born before 1730, as he was at least age 16 in 1745 to be recorded as a tithable in Frederick Co., VA, along with Thomas BAY [his father] and William BAY [his brother].All records attributed to this mythical "James Hugh" BAY appear in original records as simply Hugh, and apply to Hugh, the son of Thomas.His wife, as shown by ORIGINAL documents containing primary source information was Mary, not Jane Ann.
Early researchers estimated that his son Hugh was born about 1758, based only on what they knew of his son Robert.Early researchers had no idea of Hugh's residence before he appeared in what became Missouri.As records have been gathered about Hugh, he was clearly born earlier, as his eldest children were born in the early 1770s.He was probably born about 1748-1750.There are no known original records where his name appears as "Huey".
The younger Hugh's son Robert BAY is the person who married Mary HAMILTON. His name was NOT Robert Thomas BAY.The source of his having a middle name Thomas was a published book.A nephew of the author has stated that his uncle took his (the nephew's research), and between confusing information in that research, as well as problems by the publisher, the published work came out as Robert Thomas BAY.There is NO record of his having a middle name.
The younger Hugh's son was Samuel BAY, not Samuel Mansfield BAY.These are two entirely different men, from different BAY lines.Hugh's son Samuel had no middle name.
There are no records to connect this BAY family to a BAY family of Denmark.I've only addressed a few of the main problems with your post. Rather than try to outline all the other problems, I suggest you read the well documented book *Some Members of the 18th Century Colonial American BAY FAMILY* by Tommy L. West, M.D. (Baltimore, MD: Gateway Press, Inc. 2004).It is the best source in print for anyone who had BAY family in the United States prior to 1800.The author can be reached at dorosheffinsightbb.com