Two Mordecai students named Goodwyn are listed in the appendix to my 1996 dissertation:
Harriet Goodwyn was at the school in its final year, both terms of 1818, and has the name Braddock Goodwyn attached to her account. Susan Goodwyn was only at the school for one term, the first half of 1816, and has the name Susan Goodwyn attached to her account. I don't have much more to go on; Harriet may have been from a place called Goodwynville, and Susan from a place abbreviated "Btsbg". But their name isn't so common, maybe there will be something out there now?
Or maybe not.
Easiest name to search was Braddock Goodwyn (c1741-1820). He was from Dinwiddie, Virginia, and one of his many children was... Harriet Goodwyn (born 1795). Which might be the right age for a Mordecai student, but not for one who attended the school in 1818--she would have been in her 20s by then. So I suspect we're looking for another Harriet, a niece or younger cousin of the one born in 1795. Like I said--big family. Peterson Goodwyn, a Congressman and Braddock Goodwyn's brother, was probably a relative, but he didn't have any daughters named Harriet or Susan.
Goodwynsville was once a settlement in southern Dinwiddie County; it no longer exists.