I think you would have been correct in getting AI.
What kind of hands would have had you beat on the turn? 67,A3,63 and that's it. Neither of those hands are likely to be held by the BU as he isn't crazily loose and he did 3bet you preflop. I think, assuming he doesn't have anything really unusual with his preflop 3bets you could assume he's on a strong range, like JJ+, AK, maybe AQs. You have that entire range beat (infact, 90% equity).
My poker maths isn't flash, but I think that the pot odds you were getting to call (assuming MP3 doesn't call the AI, which he'd probably do, but that would just improve your odds) would be: $4.63 / $12.56 so you would need ~37% equity to justify a call (with the $4.63 being what remained of your stack which you could invest and the $11.16 being the amount of the pot you could win ($5.33 of your entire stack, 5.33 of the BU, and the $1.90 invested by MP3)).
If you add in the worst case scenario of the reraise (which I think would be a range consisting of just 44,55,22,76,A3) as your opponents range you still have 39.08% equity so you'd have enough equity to call. That is the absolute worst case scenario and is hugely unlikely. Highly doubt anyone but a maniac would reraise preflop with those kind of hands. Calling for set value maybe, but a reraise almost definitely not. Also, as MP3 would likely have also called the push (he's more or less pot committed on the turn with his reraise) you would only need 33% equity ($4.63/$14.03=0.33)
I think a flush draw would have been unlikely. A heart draw is consistent with the flop (ie: then passively playing to try cheaply see the turn), but then the crazy betting on the turn just would not make sense for a diamond or heart flush draw.
Overall, I would have played like this:
Preflop = Raise to $0.20 and then call the reraise if it's by a player who 3bets loose, all for set value. If I miss the set on the flop, I'd be out right there (unless it was very very cheap to see next card). Of course, if it's a perfect cbet flop with 2 low cards and a high card all rainbow, then I'd lead out with a cbet. But really this depends on whether the opponent folds enough because this cbet would be a semi-bluff, and remember bluffs ONLY work when your opponent folds (unless you hit an 8 on the turn. But that only happens ~8% of the time)
If I had called the reraise then:
Flop = Raise to ~$0.75 to extract value from your hand and to protect from a possible straight and flush draw. I think overcards and lower sets would call you and you'd get value from that.
If raise was called, Turn = again raise 3/4 pot and aim to get all in ASAP!
