My husband is a descendant of Simon Girty,Jr. Having done quite a bit of research on the Girty family, I don't recall coming across anything that specifically names any of George's children. Jame's children were James, (Jr?) and Ann/Nancy, whom he names in his will. His wife was Betsy, a Native-American. You might find more information on George's children through the Draper Manuscripts. I haven't yet been able to access all those records on the Girty family. There is quite a bit of information on him in Butterfield's "History of the Girtys", but again, no mention of who his children were, simply that he had several. It also says his wife's name was Betsey, but that may not be correct. There seemed to be quite a bit of confusion between the 3 brothers by various authors. There were at least two marriages of a George Girty in Ohio in the early 1820's - 1830's, but I am not sure which member of the Girty line they were descendants of. George was said to have died in Ohio on land owned by James on the Maumee, two miles below Fort Wayne. Goes on to say his family remained with the Delewares after his death.
Wish I could be of more help. Good luck in your research.