Ask your wife is she would feel better if you used pool store liquid chlorine instead. Odds are that she will say yes. Then, tell her that pool store liquid chlorine is usually 10 or 12.5% sodium hypochlorite and bleach is 6% sodium hypochlorite. If 10 or 12.5% strength is ok for your pool, then surely 6% will be! (It's just the word "bleach" that scares people.)