Rim and tyre width is your call. 20mm outside rim width is just what matches 23mm tyres. You may well want to go bigger, but you can mount 28's on the same rims if you want to.
I don't know if it's possible that you mounted 700C's onto a 27" rim. I'll rahther venture a guess that your female friend doesn't have enough hand strength or good technique. Some tyres are pretty difficult to mount anyway, so it's ok.