Hi, please post the first picture again so that the characters are clear. Also include a size reference. Is that some kind of corrosion at 7 o'clock? Where did the in-laws get it and when?
Looks to be a tetradrachm from the Kingdom of Bithynia (part of ancient Greece, but the territory is now located in modern-day Turkey). As far as I can see the legend reads BAΣIΛEΩΣ EΠIΦANOYΣ NIKOMHΔOY.
NIKOMHΔOY is for ‘Nikomedes’ and BAΣIΛEΩΣ his claim to kingship. There were multiple kings with that name, but the additional word EΠIΦANOYΣ (‘Epiphanes’ or ‘God-manifest’) was the self-styled title adopted by Nikomedes II. He instituted a local year-numbering system for Bythynian coins which allows them to be more narrowly dated, but yours is too worn to read the characters. It will nevertheless be from between 149BC – c.127BC.
The reverse depiction is a fairly typical “Zeus standing left, holding wreath and sceptre with eagle standing left on thunderbolt”. Lots of variants exist, but here’s a typical example:
Nikomedes I used only the ‘kingship’ title. Nikomedes II used the additional title ‘Epiphanes’ (Ἐπιφανής) meaning ‘God-manifest’. Nikomedes III used the additional title ‘Euergetes’ (Εὐεργέτης) meaning ‘the benefactor’. Nikomedes IV used the additional title ‘Philopator’ (Φιλοπάτωρ) meaning ‘father-loving'.
Also, the ‘local year’ numbering on these coins was first introduced by Nikomedes II so, if those characters are present, it’s not Nikomedes I.
I was looking at tetradrachm last night but didn't see any with such a pronounced chin or that matched closely enough. Guess I didn't look long enough.