Milliepede - as you have discovered there are clearly family links between the Webbs and the Crosses. Jemima's mother was a CROSS and her sister Mary Ann married a CROSS. Moreover, the CROSSes are millers from Croxton, Cambs. All of which is consistent with the father of Caroline's first child being William CROSS, a miller, and Caroline's maiden name being given as WEBB.
If we assume that the father come from Jemima's immediate family there are a number of possible candidates: Thomas (b 1813), William (b 1819), Joseph (b 1825) and Charles John (b 1834). Thomas, William and Joseph are unlikely, as they were all married and living with their families outside the Tottenham area in 1851. Other male siblings are dead by 1853. Charles John seems the most likely given the name and that he was a miller from Cambridgeshire. In 1851, he was working with his brother outside the Tottenham area, but could have been visiting at the required time. In 1854 he married in Wisbech, before emigrating to New York in 1856.
Although it is tempting to pin the birth on Charles John, we should be aware that there were other Webb and Cross families in the Tottenham/Edmonton area, many of whom I am sure could be traced back to Cambs.
So I think the best we can conclude about Charles John was that he was illegitimate, to an unknown father. I wonder whether the fact that she had an illegitimate child was a barrier to Caroline having a church wedding to Thomas. The continuing lack of a record leads me to doubt that they formally married.
I am still puzzled by the birth of the second child being in Dorchester. What was Caroline doing in Dorchester?
This birth was also presumably illegitimate, given that the name on the certificate was CROSS not DANIELS. I note that Caroline continues the method of giving the surname of the father as her maiden name to the registrar. Moreover, the fact that the baptism was some 4 years later seems to confirm the assumption.
If there was a marriage it must have been between 1858 and 1862, though its geographical location remains problematic.
PS I am sure you are right about 1861C. I now have her in 1841, 1851, 1861, 1871 and 1881.