Is there an authoritative source that explains where the different kanji come from and what the radicals mean? I think it's hard to tell from most of the textbooks/other sources whether a shown kanji's origin is correct or if it's made up. Does it even make sense to talk about the origins of some kanji in terms of its constituent radicals if that kanji is a simplified version of a traditional kanji?
The short answer is: No. There isn't a single authoritative source that can tell you where each and every Kanji comes from, since the complete etymology of some Kanji remains in controversy. This is actually not at all different than the state of the etymology (= study of origin) of English words.
The longer answer is more hopeful, though: there are some sources that are more reliable than others. Just like the Unabridged Oxford Dictionary is considered quite authoritative when it comes to English etymology, there are Japanese Etymological dictionaries that are considered better and worse.
I know Daikanwajiten used to be the most highly regarded Kanji Dictionary, but it's quite old, so it probably doesn't contain a lot of recent research.
After reading your comments, I think I understand better what you're trying to do, but unless you really want to learn the etymology for its own sake, you better refrain from wasting your time on it. Why? Consider the following case:
The mnemonic most often offered for 東 is that the you view the sun behind a tree as it rises from the east. It's a very cool and useful mnemonic (though the sun could just as well be viewed behind a tree when setting in the west, but that's besides the point :)).
Now you want to check whether this mnemonic is reliable so you open your etymological kanji dictionary and this is what you get:
(For reference: I got this particular one from a dictionary called Kanjigen)
So now it turns out that the kanji for East has absolutely nothing to do with trees and suns. From looking at its form on old tortoise shells scholars realized that it's some sort of bag wrapped around a stick (I admit I'm not quite sure what it was used for) which probably came to represent the meaning "east" because the word for it had a similar sound.
Now, I hope you agree with that's an awful lot harder to remember than the simple explanation of "Tree + Sun". Plus, knowing that 東 used to look like a candy, doesn't really help you to know how it's written today.
Please note that the example I gave here is not an exceptional case or anything - in fact, most of the time you'll either encounter an explanation like that (in which the modern radical components of the characters are an afterthought) or the character would just be a Sound+Meaning composition where the main radical (the one which is used for dictionary look-up) represents the general field of meaning the kanji relates to (body parts, plants, birds, etc.) and the rest of it is based off another kanji with a similar reading.
Probably get this book called 新漢和大辞典(shin kanwa daijiten), 20k kanjis there.
Which also include 漢字の成り立ち(How kanji formed)
If you forgive the shameless self-promotion, I’ve put together this simple tool to compare a few different kanji etymology websites. You quickly find out that there are lots of disagreement. http://namakajiri.net/kanjigen
I suggest A Guide to Remembering Japanese Characters, by Kenneth Henshall. It gives both the true etymology (if known) and a mnemonic explanation that is more useful to memory. It seems to be exactly what you were looking for.
My friend showed me a pretty satisfying one. It has all the 常用漢字 and also the Kanji are divided into groups 小学1-6 to 中学. It shows what original pictographs today's Kanji had, and each radical is described. Give it a shot.
It's completely in Japanese though.
http://www.kanjinetworks.com/ is probably the most reliable and thorough online kanji etymology resource.
There is an ongoing Kickstarter campaign of a book that shows you how to learn the joyo kanji through real etymologies.
You can check it out here: http://bitly.com/realkanjiworld