I can't seem to find any evidence of it online, but does anyone know where to find the ORIGINAL opening of UEA, the one with the theme song sung by Bobcat Goldthwait?

I thought the opening song was "Hit the Road Jack" by Ray Charles.

It was, but on the first season, when the show debuted along with the WB, there was an original song used instead of HTRJ. This was actually plastered over later with the "familiar" opening.

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https://en.wikipedia.org/wiki/Unhappily_Ever_After#Theme_song_and_opening_sequence

When the show first began its run, the original opening started with the "wedding photo" (even though they are moving in it) of the Malloys, with their smiles fading, and showed clips of the father leaving and walking through the slum to his new place. While walking, a man runs by him holding a TV, chased by another man who stops, takes a shooting stance, and fires a gun at the thief. The next clip shows the father as he walks past the first man lying face down, TV near his hands, as he enters his apartment. The theme song played over the opening was Bobcat Goldthwait (and possibly others) singing "We married young, because of cupid. And had three kids, but we were stupid. She kicked me out, she's not my honey. But she still wants me, when she needs money. Now I'm alone, come rain or sunny. But who needs love? I've got my bunny." In the final scene of the final episode, this is the song Jack sings with Mr. Floppy, but with slightly modified lyrics. "I married young, because of cupid. And had three kids, but you were stupid. I could've been rich, instead I'm a loser. But at least we're happy, 'cause you're a boozer. Now I'm alone, come rain or sunny. But who needs love? I've got my bunny."

Beginning with the second season, the series' theme song was "Hit the Road Jack" by Ray Charles; the song is a reference to Jennie kicking Jack out of the house. The opening is a sequence of bizarre events from the first season and the male vocals are lip-synched by Floppy while the female vocals are lip-synched by Jennie, Tiffany and Maureen for Seasons 1 & 2, Jennie and Tiffany for Seasons 3 & 4, and Tiffany, Jack, Ryan and Ross for Season 5. In reruns and syndication, the Season 1 opening was replaced with the "Hit The Road Jack" opening with clips from the show.