M.,
It sounds to me like your daughter is having a hard time feeling the little tickle that happens that lets you know you need to pee. It might be helpful to talk to her a little more about the biology behind peeing. Like that her body needs to be clean, so the icky stuff goes into her pee pee and there is a little cup inside of her called a bladder that gets full. When the cup is full, her body tells her it needs to be emptied with a little tickle.
I think, in general, girls are easier, but that doesn't mean that for your specific children that will be the case. It may just be that she isn't quite ready yet. Maybe you should take a month off of the potty training and come back. Every child develops differently, as you know as an educator, so timing can be everything.
It also occurred to me in your post that you may be running out of patience with her. She will pick up on that and it will become a power struggle, if it hasn't already. So keep taking her to the bathroom and sitting her on the toilet. Sometimes, you have to do that for a long time. One thing we did was print out a blank table in Microsoft Word and the kids got to put a sticker in the square everytime they actually put pee in the potty. When they filled up the squares (I think we did twenty-five boxes) they could get a big treat. The son's was a Rescue Hero and the daughter's was fake food or a baby doll thing. Basically, anything they wanted that was less than $10. So if they had an accident, I didn't, or tried not to, yell. I just said, "Oh no, you don't get to do a sticker for that one."
And don't worry...most kids don't head off to college in Pull-Ups, and there will be a day when you barely remember changing diapers! Good luck!