Research Notes:
1602/3 Elizabeth Ring was baptized at Ufford, Suffolk, England. [1]
She may be the same Elizabeth who arrived in Plymouth with her mother. However, she seems to have been as much as ten years older than usual at marriage and would have been nearly a decade older than her second husband. If the Ufford family is the one that came to New England, it is possible that the 1602/3 baptism is for a daughter Elizabeth who died young and the wife of Deane and Cooke is a subsequent daughter of the same name.
[1] John Insley Coddington, "The Widow Mary Ring, of Plymouth Mass., and her Children," The American Genealogist 42 (1966), 193-205, at 198, [AmericanAncestors].