I have made an executive decision until original records can be examined:

The information regarding births, marriages, and deaths in Casalnuovo Monterotaro comes primarily from the records captured by the LDS Church and made available freely to the public. The birth and marriage info for 1809-1865 has been indexed and a searchable database made available on FamilySearch.org. The info on Vincenzo Melchoire and Maria Carolina Paola Parente comes from this indexed data.

Indexing means that someone read the microfilm images and recorded critical data into the database regarding what they read on the images. I suspect that an error may have been made in indexing the marriage record on Maria Parente.

If you search the database for "Maria Carolina Parente" you get exactly 2 hits - her marriage to Vincenzo Melchiore and the birth of Carmina Maria Socci to Maria Carolina Parente and Vincenzo Socci.

If you search for Vincenzo Melchoire you get only the marriage in CNMR. And the other hits, in other locals, are with different wives.

If you search Vincenzo Socci, you get several additional births with "Maria Parente". (Only the one shows the middle name Carolina) Also, the births are consistent with (follow closely, but no overlap) the marriage date of 1811.

CONCLUSION: I have decided to change the marriage info so that the husband is "Vincenzo Melchiore Socci" and attribute the births with Vincenzo Socci to Maria Carolina Parente - daughter of Giuseppe and Susanna Ambrosiano.

I will continue to research the issue and will get a look at the original film as soon as is practical.

2018DEC04: Socci name confirmed from original film