Hello everyone! This is my first post here, though I've been lurking for about a year now. I always hoped I'd have some etiquette dilemma that the e-hellions could help me with, and I finally found one.

It's kinda long, sorry.
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The background: I work for a company where each employee is assigned to a two-man team, making widgets at a given location. Every day, you and your partner must be on location and independently produce a widget to deliver to the customer. The widget must fit a set of specific standards, which depend on location, circumstances, and who it is being produced for. This is at odds with the general character of the widget, which completely depends on the opinions of the person creating it. Your widgets must be checked against standards every day, and at the end of the project, all the widgets end up as a thingamajig. Job ratings are tied to how well your thingamajigs satisfy the standards and the customer, and how accurately they reflect reality.
Currently, I am assigned to location N, which isn't particularly different than any other location we could be assigned to (though they all have their own quirks). Co-worker A has been working this particular location as a widget-maker for a fairly long time. He was assigned to work on the widget-reviewer team near the end of the last project, and I and my partner were sent to take his place. He no longer has any official connection to or responsibility for thingamajig production at this location.
The problem: A cannot stay objective when reviewing our widgets because we are at "his" location, which he may or may not be reassigned to. He constantly critiques the subjective portions, which he has no right to do, first. Also, there is no way he can determine how accurate we are being when he is not here. These decisions are entirely up to me and my partner. On the one hand, I am glad for the extra set of eyes on our widgets, because mistakes are always possible and he does, in all fairness, produce very nice thingamajigs. On the other, many of his requests are actually demands that we conform our widgets to fit with his idea of how a thingamajig should be. There is enough flexibility in the standards that he can give bad reviews for not altering the widgets to incorporate what he suggests. A is a forceful presence. I found him very abrasive even before he was a widget-reviewer, so with his new position, I am willing to bend to his demands just so I don't have to hear about them. My partner would prefer we don't listen to A at all and just get on with doing thingamajigs my way. He thinks I am too easygoing, by far. He's probably right.

A few days ago, A contacted me about a particular doodad on my widget. He was of the opinion that the doodad should not have been placed there and demanded I take it out. After reviewing the doodads in previous thingamajigs, I went ahead and removed it without consulting my partner, even though he was the one who put it in. This isn't entirely unusual, but asking beforehand is a courtesy I should have extended to him.

He was put out with A for suggesting the removal, and with me for not consulting him. I had been content to leave it in, though not confident it was necessary, before A's call.
My partner and A
really dislike each other. We are all officially at the same level. Nominally, I am in charge at this location.
So I suppose my question, in short form, is this: How can I tell someone, with more experience at a given location making thingamajigs, that I am perfectly capable of making them without excessive input, and to kindly refrain from commenting except on standards violations? I may have to work with A again in the future, as I am one of the few people left at this level that will work with him at all.