In various places her name has been spelled as Annloire, Anneloire, Ann Louisa, and Ann L. The Remington genealogy from Virginia Adair (and given to the Roger Williams Family Association) has Louisa, b1800, marrying George Moore. It also lists another sister named "Samiloire" who supposedly also married George Moore. According to James N. Arnold's transcription of the Cranston records, the two were married on the exact same date, but two years apart. It seems clear to me that this is the same individual, and that there must have been an error in the transcription, perhaps recorded some time afterwards. In the 1860 Federal Census, George & Ann L. Moore are living in Providence, RI. Her age fits "Louisa" in the typed genealogy from Mrs. Adair.
Also, the RI Cemetery Database has her name as Ann Louisa (Remington) Morse, d/o Capt. Charles Remington, and w/o George Morse. Possibly Moore was misread on the gravestone as Morse.
However, their marriage announcement in the Providence Phenix identifies the couple as Ann Louisa Remington & George Morse.