Hi there,
Are you certain that these two marriages were for the same bride?
Does she sign her name each time, have you checked with the good folk at RChat's Decipher board that the signatures are likely confirming same person each time?
Have you written to the particular church and asked them to check the church register to see if there's any notations made by the Rev in the margins, or perhaps in his diary, or in any other contemporary records re either marriages?
Have you checked for any notes made by the clergy when either of the two children may have been baptised?
Have you checked local newspaper mentions over the course of the years between the two marriages for any comments about negated marriages?
Oops, and have you triple checked for the demise of the first husband
I am in NSW Australia, and I am aware that many of the females in the penal era (transportation of convicts to NSW effectively ceased 1840) and basically until civil registration commenced (March 1856) were known by the surname they used when they landed, if coming from overseas (either as prisoners or as settlers, or as the spouse of the garrison forces etc etc etc). So, even after marrying in NSW, the women often retained their surname rather than take on the surname of their new spouse. Perhaps that also occurred in other British spheres of influence, or perhaps it is something peculiar to NSW.
Cheers, JM