Jean, I take it that you have a Loyalist in your family. One of my husband's great-grandfathers, born 1748 in Raloo, Larne, Northern Ireland, had migrated to this country and was a Lt. Col in the Georgia Militia. Naturally, he fought for the Brits.
After the War, he returned to Northern Ireland to petition for the land he had lost but he apparently was not completely successful in his endeavor because he instead returned to South Carolina by 1802 and had decided that he wanted to be a part of this country. He received a pension from the British Government that came by ship at the prescribed time.
You might look for that sort of thing as well as see if he was listed as a resident alien during the War of 1812 as his relative was. We could tell the time departed, the time he was there, as well as the time he returned due to land. The departure showed the children born in Georgia; the time in Ireland listed two of the children being born in Ireland; the ship registered his pension being delivered to Kershaw County, SC by 1802.
Hope that gives you some idea of things to look for.
You might Panton & Leslie, a company with strong loyalist claims. The Spanish records are good but there are other sources as well. The Spanish records, at least part of them, can be found at the Florida Archives; the Archives are online.