What route to take in converting ethanol to crotonic acid?
Allylic bromination and subsequent hydrolysis might be replaced by an allylic oxidation of the butene using selenium dioxide - if that's inorganic enough for you ;)

But I'm wondering whether there's a shorter way. What about the Grignard reaction you described, followed by oxidation (PCC on silica or manganese dioxide) to 2-butenone. Subsequent bromination with bromine in hydrobromic acid should yield an $\alpha,\alpha'$-dibromoketone which, upon treatment with base (Favorskii rearrangement) and, eventually acidic workup should yield crotonic acid.