The Louisiana Civil Code of 1870 (it was revised between 1868-1869, but enacted in 1870) applied specifically to civil cases (i.e. disputes between private parties); it's organized by topic area, and is there to keep people from having to comb through every law ever passed that has to do with civil cases. The Revised Statutes of 1870 gathered all the laws of "general character" into one place, for the same reason. The difference between the two was almost certainly an error.
In general, there is one official version of the law; other versions are a convenience. The official version normally defaults to the individual laws passed by the legislature (which are organized by date, not by anything useful for finding relevant laws), but that can be changed by statute. In this case, the Revised Statutes contains section 3990, which says
in so far as there may be any conflict between the provisions of this act and any provision of the said Revised Civil Code and Code of Practice, that said Code shall be held and taken as the law governing
So, the Civil Code took precedence.
Your revisions of 1876 and 1882 were not successor laws; rather, they were compilations of the Revised Statutes and Civil Code of 1870 with the amendments to those that had since been passed. The Revised Statutes from 1876 were really the Revised Statutes of 1870, modified by later laws (that didn't touch the divorce provisions). Likewise, the Civil Code from 1882 was really the Revised Civil Code of 1870, modified by later laws. The Civil Code of 1870 still took precedence over the Revised Statutes of 1870, so the divorce provisions of the Civil Code were authoritative.