Staining already stained wood
In general, finish coats will not absorb any stain. The finish seals the pores of the wood preventing anything from penetrating.

True stain can only be put on wood that does not have a sealer on it. Where you sanded, you removed the sealing finish coat. That let the stain penetrate and darken the wood more than the surrounding areas.

The only real fix now is to sand off the finish from all of the visible surfaces, pre-condition, stain and refinish. You may have to do a little blending or feathering on the edges of the areas that have already been stained.

The only alternative is to use a poly-stain. This is really just a heavily tinted surface coat rather than a penetrating stain. You would need to make the color much darker to cover the variations you now have. Probably not the best idea.