"Vakula the Smith" is given Opus 14, and as far as I can tell "Cherevichki" has the same Opus number. Is this correct and is it normal to reuse the same number for extensive revisions like this?
According to Wikipedia:
Opus number is the "work number" that is assigned to a composition, or to a set of compositions, to indicate the chronological order of the composer's production.
Also, indeed, Vakula the Smith is Op.14 but note that
Tchaikovsky did not permit it to be performed at other theatres. Dissatisfied with the opera, Tchaikovsky revised it in 1885 as Cherevichki.
It looks like Tchaikovsky erased and replaced Vakula the Smith with Cherevichki after doing some modifications, so Cherevichki doesn't counted as a new composition and does not have its own opus number.
Also note that opus number assignment isn't always consistent. Sometimes it doesn't follow the chronological order. Sometimes it is assigned by the composer, sometimes by the publisher... It also happened that opus number of a revised work were distinguished with a letter.