Michael VIII was cunning, and diplomatically skilled in a way I think was OTL only matched by his descendant Manuel II (who despite ruling a polity on the verge of death bought it another 50 years through sheer will and effort) in diplomatic skill. Had he been directly followed by a military man, like Andronikos III, or by a polyglot-polymath diplomatic master like Manuel II, the Empire would have gotten fully back on it’s feet.
Honestly, the fact that Michael VIII was so capable as a person and not a complete incompetent (though had he been he would never have been able to create the longest lasting dynasty in Roman history, a fact which is certainly ironic) kind of makes his failure even worse.
- Blinding John IV Laskaris, thus losing himself the Akritai and being known as a usurper.
- Abandoning the Anatolian lands in favour of Europe, which without the Akritai began to fall rapidly.
- Forcing a union between the Catholics and Orthodox that destroyed the religious and cultural identity of the Empire and left him and his dynasty hated by the citizens until 1453.
The thing is, those were severely damaging to the Empire, so no matter how capable Michael VIII was, it still very much damns him in hindsight in my eyes. But here's some points about that:
1) The blinding of John IV. If that were the only thing he did, that could've been smoothed over in time.
2) He didn't fully abandon Anatolia. He did campaign there. He just focused on Europe far more than he probably should have in hindsight. Also, in fairness to him, he did have to deal with a Latin invasion in the last years of his reign, so there was good reason to focus there. And of course, the enemy that would ultimately destroy the empire wouldn't even emerge until Andronikos II's reign. It was also hard to judge the nature of the threat the Turks faced with the fracturing of the Sultanate of Rum during his reign.
3) The Forced Union really, I think damns him fully. This really fully solidified the divisions within the Empire, however, I've yet to see any sources pointing toward the union affecting the public's perception of the dynasty right up until the fall of the city. The Union was abandoned right after Michael's reign and his memory was damned if my memory serves me (which it might not; my family isn't known for having a good memory).
Ultimately, you can have the potential to be a fantastic emperor, but still end up a disaster for the Empire.
As for Andronikos II, I know very little about him outside of his track record, so it's really hard to judge him on a personal level. Maybe he would've been a better emperor had he ruled in better times? Or perhaps not.
However, the tone of his reign was decided by the actions of Michael VIII. Had Michael VIII not pushed through the Union, Andronikos II would not have had his administration paralyzed right from the outset by the need to clean up the divisive mess left in it's wake.
So no, I don't think that had Andronikos III been emperor in 1282 the Empire would've avoided the disasters of his grandfather's reign as his administration would've been just as hamstrung by the legacy of Michael VIII.
Also, the Angeloi did not break Manuel Komnenos's empire. That was actually Andronikos I Komnenos.