I have a slightly skewed perspective of this, because this *is* normal in my group. I do think it's a generational thing. I never thought it was rude until I came on here and realized other people do, and now I look at it as more of a "know-your-audience" type thing. IMHO, being polite is about not offending the people you're with. If you know for a fact that answering the phone won't offend someone (as in my group), then while it's rude from an outsiders perspective, you're not offending anyone in your group, and to me that's what's really important. (Though I realize this is an etiquette board, so I know I'm probably alone in saying that it can be acceptable at times.)
However, that's not the situation in the OP. There has been once or twice where I realized I was with someone who *would* get offended, so I'd pick up the phone and say, "I can't talk right now, can I call you back later?". If I didn't, I'm sure the person I was with would have tapped me on the arm and whispered, "You know, I was really enjoying spending time with you. If your call's important, I can come back later. If not, do you think it would be possible to call PersonOnThePhone when we're done?"
I've also been like Priscilla and *had* to talk now, but from the OP, this isn't a one-time-thing. I'd have given Kate more credit here if Priscilla was someone who would usually understand, but was in the middle of something big that she needed to talk to her best friend about. Since it's some that seems to be a common occurance, I think it may be time for Kate to set up a system. Something along the lines of, "If I don't pick up the first time, only call back if it's an emergency. If not, leave a message and I'll get back to you ASAP."
Though I'm not sure it would work with Priscilla, I feel like it's time for Kate to set up some boundaries in their rel@tionship. This is coming from someone who sees no topic of discussion as something that you can't talk to your best friends about, and would drop anything if my friends needed me, but this would get to even me. Is it possible that Kate is getting tired of Pricilla, too, but is afraid to do anything about it?
As for the talking while driving thing, I'm far, far less alarmed by this than texting while driving. It's not safe, but I'd much, much rather a form of communication used while driving that used ears and one hand only over the "Drive with your knees, hands on the phone, eyes going back and forth" type method. I understand the legalities, but since this isn't a legal board, I figured I'd speak from personal experience there.