In addition to other suggestions, you could consider a chess variant that may even the playing field.
Chess960 (https://en.wikipedia.org/wiki/Chess960) [previously called Fischer Random, but renamed to avoid potential conflict/discussion over Bobby Fischer who invented it], for example is a variant that randomizes the positioning of the back-rank pieces. Unlike other randomization variants, this one strongly attempts to keep everything else about the game the same. The rules of piece placement are:
-The two sides are mirrored, as in regular chess.
-The king must be between the two rooks [this allows for castleing, which involves moving the king to the 'traditional' kingside or queenside castleing positions].
-The two bishops must be on opposite colours.
This leaves 960 possible positions, which can be chosen at random through various means (check the wikepedia page for details).
The benefit of chess960 in this case, is that it eliminates some of the advantage inherent in opening position theory.
By the midgame, a typical Chess960 game looks like a regular chess game (except perhaps for some oddly placed pieces here or there). Ultimately it opens up like a regular chess game, but you can't memorize any opening lines. For a 1500-1900 matchup, opening theory likely makes a significant edge between the two of you. Of course, there is some small learning curve to starting to play chess960, but as you are both learning it for the first time, you will both have that curve together. Of course, a skill difference would still exist, so even with Chess960 it may be required to still give your wife a rook/ minor piece for the full handicap.
A particular copyrighted variant that creates an even greater randomization aspect, is "Knightmare Chess" http://www.sjgames.com/knightmare/. This game introduces cards with various impacts on the game ("This turn your pawn can move twice, etc."). The random element decreases the net impact of a skill differential somewhat, as luck plays a fairly large element.