Hippie and I are the same age =O.
Anyways: I don't fight Peaches often but i'll go with what I saw your friend doing. He (I assume) had to basic approachs; Fair and Dair.
He used the Dair either more at a distance, or when you were both in the air. He used the Fair when you were a medium range (just enough so that he could catch you with the hit frames). One thing I'm not sure you get much work in is powershielding, either learn it or use it if you are hiding it from us ><. The Fair pulls Peach towards you, so a powershield could lead to another beastly OOS UpB like you pulled off first stock, or a grab (which you didn't do too much).
When he does the Dair, you shield it, but then you have a weird spot dodge reflex which you are aware of. Since your opponent didn't do any grabs (pretty sure I didn't see any). You could have thrown out the spot dodge altogether. However, i know from experience that some stuff is just reflex, so you'll just have to condition yourself to use it sparingly (if at all), no biggie.
Practice teching on Luigi's Mansion sometime (offline) and get the feel for it. If you have a friend, go to corneria, if not take a CPU to LM, because it's bound to hit you into a ceiling. On Corneria, mix up between teching the wing, and bouncing off the wing and teching the ground (that's hard to time if your opponent is waiting for an attack). That way, you can add a little variable to your game there.
I think that's it, in my lame opinion of peach, I think that you should refrain from combos against her because she seems to be able to do all these attacks really quickly to throw you off. Nair plays an even more important role in this fight. Back up a little read your opponent, but at least watch your own vids and snapshot your opponent, whom i presume isn't going to radically change their game next time you fight.
)