British Rear-Admiral Charles Holmes Offspring

I am looking for information regarding British Rear Admiral Charles Holmes (my 6th great grandfather). Specifically, any information on offspring he may or may not have fathered. There is little genealogical information on Charles offspring, and it appears his line ends with him. However, my research has discovered Charles may have fathered a son Thomas Holmes (born circa 1759 in Quebec?; died c. 1830 in Plattsburgh, NY; married a Mary C?), but there is also reference to an illegitimate "child" (gender unknown) allegedly the result of a scandalous affair with the famous brothel owner Mother Jane Douglas in England. The affair occurred sometime after 1746. As her Wikipedia profile suggests: "Around 1746... Douglas herself became pregnant; the child was thought to be Lord Fitzwilliam's and was the subject of much debate, although Rear Admiral Charles Holmes, another of Douglas' lovers, later turned out to be the father." I am looking for any additional information anyone might have on who the "illegitimate child" might be and/or if Thomas is that child; or any information on Thomas himself if he is not the "child" of Charles and Jane Douglas. Thanks in advance for your assistance.