I don't view ships affected by ion weaponry as actually performing a manuever.  They are simply drifting.  No manuever is selected, therefor there is nothing for the R2 unit to affect.

As for the R2 unit for the critical hit, I honestly think the R2 overrules the damage effect on the conflicting manuevers.  Determination outright cancels damage cards, why wouldn't the R2 unit still allow green moves.  The critical card would still get to affect other manuevers, just not those adjusted by the R2 unit who's role is to make those manuevers easier on the pilot.  The determination card cancels a small subset of critical damage cards.  Why wouldn't the R2 unit also cancel a small subset of damage cards (or in fact a portion of the critical effect while the damage remains).  Sure, determination outright tells you to cancel the damage, but the R2 outright tells you to treat all of those manuevers as green.

If anything, couldn't they cancel each other out.  So the manuevers affected by both cards are simply back to their default (white in most cases).

Think of it this way.  A white turn 1 is made easier (+1) by the droid turning it from a white to a green.  The critical damage would typically make the manuever harder (-1) by turning a white into a red.  So white +1 = green.  White - 1 = red.  White + 1 - 1 = white.  Certainly no presidence in the rules for this, but it would make sense to a degree.  The critical damage makes the manuevers harder, but the droid is still compensating to make the manuevers easier.

 I'm typing up the post for this topic on the FAQ I made as we speak. The stance I'm taking is that this is still highly debatable and could go either way though we seem to agree that the damage OUGHT to take precedence. We just can't definitively prove it from the rules. However, one additional piece of evidence I'm going to include (and determine more in favor of damage taking precedence) is that the R2 says 'may treat…' whereas the damage card leaves out the 'may' and just commands you to treat hard turn maneuvers a certain way. Similar to 'forbid' I feel this overrides optional abilities. It's as if the game is telling you "I don't care what I said you could do before, I'm telling you to make this decision." Please….discuss.

 The ion hit means you don't even use a maneuver dial next turn, so YOU aren't 'performing' a 'maneuver' at all. As others have said, it's just a small drift while your ship's systems (and likely R2 as well) 'reboot'. And the ion effect card states 'owner moves ship AS IF performing a white 1 maneuver.

Baphomet69 said:

There is no "performing" in relation to movement. In this game, you can "perform" attacks or actions. Maneuvers are not "performed", they are "executed". The ion card specifically uses the word execute. My opinion: they shouldn't have, because I think they didn't mean it, as evidenced by the fact that the first line of that paragraph states: "moves the ship as if it were assigned a [straight-white-1] maneuver." It seems to me that they want ion cannon to move the ship without the pilot actually piloting it, but by using the word "executes" in the following sentence, they clouded the issue.

 Performing/executing…geez. Tell me that ain't rules lawyering.

Key words are AS IF. 

Baphomet69 said:

I agree. "As if" should be the most important part of that card. I'm just saying that the term "executing" gives the possibility for one to interpret it differently.