Hi GypsyB,
Just thought I'd mention, for what it is worth, that there is an earlier connection between the Adams and Coote families.
A Jemima Coote baptised 8 April 1764 at Shalford married William Adams 18 Nov 1788 at Gt Waltham, Jemima's parents were married in Terling.
I hesitated about mentioning that marriage but thought I would just in case it could provide a clue, the couple by the way are my Gt X 3 grandparents.
Regards.