Hello.
Here (briefly) is a possibility for you to consider.
On the 1851 census there is only one "Caroline" born in Plymouth who was married and living in Hull. She was Caroline Jackson aged 42 married to John Jackson (aged 45 from Ashby, Leicestershire). One of their children is called John Ward Jackson aged 15.
On the 1841 census there are two children living with them with the surname Ward. John aged 5 and Elizabeth aged 10. They also have a daughter called Sarah Jackson who is 1.
It looks, therefore, as if this Caroline originally married someone called Ward and had two children in 1831 and 1836 during that marriage. It then looks as if she married John Jackson and had more children. In 1861 and 1871 she is shown as a widow.
Given that she is the only census entry that meets all of the criteria specified (Plymouth, Hull, c1809 and married twice) it seems to be a strong possibility that this might be the lady that you are looking for.
DS