Did the Hamilton family keep in touch with Fanny after she left?
Unfortunately, with how hard it is to get access to the Hamilton family correspondence, let alone transcribe a lot of it; the answer is not so entirely certain. Nothing I have ever found suggests so, but I also have not transcribed every - or even half - of the letters the family wrote. Not to mention, it is a fair possibility any correspondence with Frances or mentioning her could have easily been destroyed for privacy or just lost to time.
I find it hard to believe Elizabeth or any of the children would have completely cut ties with someone they had lived with for ten years and described as family, though. [x] The only thing that could possibly suggest so, is the fact that James knew a bit about Frances' life after she left, but he very well could have just heard it circling through the news (Bold text is mine);
She was educated and treated in all respects as his own daughter, and married Mr. Tappan, an eminent philanthropist of New York.
Hamilton, James Alexander. Reminiscences of James A. Hamilton: Or, Men and Events, at Home and Abroad, During Three Quarters of a Century. United States, C. Scribner & Company, 1869.
I have heard the misconception that James was one of the only kids to still cherish Frances because his own daughter would later be named Frances ‘Hamilton’ Bowdoin (1813-1887), but that is realistically not the case as James' wife, Mary ‘Morris’ Hamilton, had a mother named Frances ‘Ludlam’ Morris (1766-1852), and it was likely her namesake instead of Antill's.
I believe there was a historian who seriously suggested that Frances officially departed from the family to live with her sister, Mary Antill, due to the Reynolds controversy catching publicity because it was during the year of 1797. And while that might actually provide reason as to why it isn't known if Frances kept contact with the family or not, perhaps severing ties due to the public shame—I still wouldn't full-heartedly believe that with what lack of evidence remains.
