Mary, While I don't believe that Thomas and Celia connect to my TYNES line I too have long believed that Sarah (TYNES) ATHERTON was their daughter. I have now come to believe that Thomas must have had an earlier wife, possibly a PRUD[D]EN. The proof is a bit complicated, and I will not attempt to provide all the details, but bear with me.
Nathaniel TYNES, grandson of Thomas, died intestate in 1803. His estate was divided among nine blood aunts and uncles (or their heirs). Four of the heirs were his mother's sisters and five were his father's siblings.
Penelope (ATHERTON) BRUNSON was, as her mother's only child, was entitled to a one ninth share of the estate.
Penelope is also mentioned in her father's will of 1787 as being "ye true and only heir to the same [a half share of land in Bermuda] being descended from Peter PRUDDEN of the afroesd. island."
For Penelope to inherit a full share of Nathaniel TYNES' estate she had to be Sarah (TYNES) ATHERTON's only surviving child.
For Penelope to be "ye true and only heir" of Peter PRUDDEN Sarah (TYNES) ATHERTON had to be the descendant of Peter.
Celia (WEST) TYNES, therefore, could NOT be Sarah (TYNES) ATHERTON's mother. If she were the PRUDDEN "connection" all her children would have been heirs to the Bermuda land and, I believe, Penelope would have no claim on the property. In fact it was Jeptha ATHERTON who leased the property in 1761, shortly after Peter PRUDDEN's death.
While I realize there may be some holes in this proof I do believe that it clearly raises the STRONG possibility of a first wife for Thomas Sr.
I would be glad to have someone to discuss this with further as I feel the PRUDDEN connection may prove fruitful for all TYNES researchers. Please feel free to contact me directly and I'll be glad to provide you with all the details and you can make your own judgement.