Please recommend a women's wide cycling shoe.

Not sure I can be much help. I have the opposite problem--long, narrow feet (women's 10 1/2 in most running shoes) so usually only men's shoes fit lengthwise, but my feet are way too narrow for them. I was really happy with a pair of Sidi bike shoes I had several years ago. As I recall, they were "men's" but came in different widths, so I was able to find a pair that worked for me. So maybe they would have women's shoes in different widths, too. Kind of difficult to find and not the cheapest, but very good quality. I wore them in very hot, wet conditions in the tropics and they lasted several years.