"...information on the certificate confirms that it is my Jessie again. "
Do you mean that the names of parents that Jessie m. 1907, and Jessie m. 1919, gives on the two marriage certificates are the same names for parents. If not, what information confirms this.
I am not wanting to be pedantic, but you have not stated this specifically.
Also, who are the witnesses on the later certificate........and might presumably know something of Jessie and her recent domestic history?