Close examination of Charlotte with a jeweler's loupe shows that the lock plates on either side are marked "T.Barker." The barrels are marked "Belgian laminated steel." A quick search revealed this:
Shotguns marked 'T. BARKER' were sold by various hardware store and catalog stores in c.1880-1910 (or so). They were generally imported from Belgium and distributed by the H&D Folsom Co. Look for the telltale Belgian proofmark underneath the barrels and on the water table (flat part of the frame where the barrels meet the frame). The proofmark is the letter 'E' over 'LG' in an oval or variant thereof.These shotguns were designed to be utility shotguns and were low priced when they were new. Nothing has changed today, and their value is strictly whatever somebody will pay to have something hanging on the wall. Under no circumstances should a T. BARKER shotgun be fired. The barrel construction is almost certainly a twisted-wire construction and the pressure curve of modern shells, even "low-brass" can certainly cause the barrels to come apart.
You can see them priced at $200-300 on some auction sites, but they rarely sell. A more realistic value would be $100-150 in really good condition. I have had mine checked by a good gunsmith and do shoot hand loaded, full length brass shells loaded with light black powder loads. NEVER shoot smokeless shells in these guns.