First, stain/dye will not work when a finish has been applied. All old finish(not necessarily old color) must be removed for new stain/dye will work.

There is a newer product called gel stain that is sold for applying over old finish. It does work, but it works because gel stain is more a paint than a true stain.

Use stripper---the chemical kind. 'Green'(non toxic) will work, but may take more than one application. Use small brass brushes to get old finish/stripper residue out of nooks and crannies.

Clean the wood after the last application of stripper following the directions on the stripper container.

All that stripping and cleaning will raise the grain of the wood. Hand sand the surfaces smooth. You must hand sand because machine sanding will easily sand through any veneer(a thin wood coating glued to the substrate wood). Veneer was/is used to make expensive wood used in furniture less expensive by using thin sheets.

Use a good stain/dye---the stuff sold in home improvement stores is not as good as the better stuff sold in woodworking stores.

I would be delited to advise you if I were looking at the items. Reabilitating often turns out better than refinishing on older items. I suggest you take them by a good paint or woodwork supply store. Call around to find one where they have someone to advise customers.