I should not have been reading Wilcox' Portrait of a General again. Everyone knows about the American Revolutionary War and Clinton's role in it, but his family life was a lot more... interesting if you ask me. Sorry for the cheap content, but I just couldn't resist:
(The answer is yes. Calculating Clinton's various absences travelling and at war, John Baddeley, his quasi-stepson, is the one child of whose life and development he would have been able to partake the most- excepting John's first 18 months, when Clinton was in South Carolina, he was almost constantly present in his life afterwards, excepting two travels to Switzerland in the 1780s. By contrast, Clinton's children from his marriage to Harriot Carter spent almost the entire first decade of their lives only seeing their father sporadically (posted to Gibraltar, emotionally unavailable for a year after his wife's death, travelling to mainland Europe, American War of Independence), and those he later had by Mary Baddeley were still very young upon his death, the youngest having just turned a year old.)
...Not to speak of William Henry (b. 1769), son of Henry (b. 1730) and brother of Henry (b. 1771) and William Henry Clinton Baddeley, defacto step-grandson of Henry (b. 1730) and defacto step-nephew of Henry (b. 1771) and William Henry (b. 1769), and half-nephew of Henry (b. abt. 1781-83).
And for good measure, why not add Henry Dawkins (b. 1765), son of Henry Dawkins (b. 1728), and father of Henry Dawkins (b. 1788), the latter of whom is the grandson of Henry Clinton (b. 1730)?
Elizabeth Carter's official reaction to learning of her brother-in-law's new partner: "The General went to see Mrs. Baderley. [...] Very unhappy."
O, Augusta... Remember all the Henry Dawkinses?