Definately a wood-splitting wedge, without the handle for some reason. The whole tool would look similar to an axe. Used to split wood rounds (sections of trunk or branch) into smaller pieces for the fireplace. Should be a hole underneath it where the wooden handle would have fit in.
There are similar-shaped splitting wedges, but those are typically smaller than this. Splitting wedges are solid, have no holes for handle attachment. They are placed in the crack already started then hit with the hammer-portion of the splitting maul. For very large rounds, several wedges can be used together to assure the round splits completely.
I'd tentatively agree the small cup would be a crucible for melting lead or tin. The lip would assist in pouring the lead or tin into a mold, such as for making lead weights or for making lead bullets. After the mold had cooled, it would be split and the newly created lead weights or bullets could be trimmed for use from any excess lead to make them more aerodynamic. Any lead left over would be used again and again.
Seems to be from 2 different centuries here. The lead crucible would be from the 1700-1860 period, when automation made it easier and cheaper to buy pre-formed bullets. The splitting wedge looks to be mostly iron, which most recently has been replaced with a variety of cheaper and lighter components, including fiberglass. If iron, then likely from 1850-1950 period.