Regardless of whether or not Padme was Force-sensitive, it's clear that Leia is. That's why she was able to hear Luke's call for help at the end of Empire Strikes Back. So while she may have only been in her mothers presence for a mere moment, it's possible that the Force imprinted her mother's spirit onto her. She was also in the womb for 9 months so it's possible the Force was working its magic there as well.
Besides, when you have memories of your infant years, they're not exactly clear. All Leia says is that Padme was beautiful and sad. She was certainly looking both of those things throughout the entire film.
Plot hole filled. Oh yeah, and that was one of the greatest movie experiences of my entire life.
laz