Perhaps the best way to answer this question is to just focus on your examples and why they feel so wrong to me as a native German speaker.
- "Ich würde nicht von diesem Regen durchnässt sein."
This is very odd.
You can actually use "durchnässt" without the "sein".
"Ich wurde von diesem Regen durchnässt."
"Ich bin von diesem Regen durchnässt worden."
I cannot come up with a reason I would want to say your sentence.
Would I ever use "würde" as an auxiliary verb with "sein"?
Let's look at what you think it means in English:
"I would not be drenched in this rain."
A slight change of would not be to would not have been has changed the example. Could this sentence still be meaningful, if the "sein" from first example and "gewesen" from second example is removed?
I certainly would feel much less startled about
"Ich würde von diesem Regen durchnässt."
Would need to combine this with something. Such as
"Ich fürchtete dass ich von diesem Regen durchnässt würde."
- "Ich wäre nicht von diesem Regen durchnässt gewesen."
That too sounds weird. So let me try to go from "ich wäre" to "ich war" just like above I changed from "ich würde" to "ich wurde". And I think there is your answer emerging from the fog! But let's first play it through here:
"Ich war nicht von diesem Regen durchnässt."
Why do you even use the negative here? Doesn't that rather serve to confuse? Shouldn't you, if you want to contrast two words in their function cut out all the clutter and look at it in their simplest example possible?
Your translation also seems to be missing something: "I would not have been drenched in this rain." You mean to add some "If" clause in front? Like "If I had only left an hour earlier, I would not have been drenched in this rain." -- "Wenn ich nur eine Stunde früher gegange wäre, wäre ich nicht von diesem Regen durchnässt geworden."
Now I come closer to your example. But I need to use "geworden" not "gewesen", because it happened to me, it is not my essence.
- "sein" vs. "werden"
- "gewesen" vs. "geworden"
I thought "to be = sein" verb conjugation is applicable to becoming something. For example:
"Ich wäre kein Lehrer gewesen."
No! This doesn't sound right again! And I don't know what you intend to say.
"Ich wäre kein Lehrer geworden."
You cannot logically put into question your being a teacher, but your becoming a teacher.
"I would not have been/become teacher."
See, in English to, "I would not have been a teacher" doesn't seem logical, you'd have to say "become". That becoming is what happened in the past not your being.
I am sure if you
- simplify your examples
- cut out all words that are not relevant
- but complete your example so it's a full sentence, not just a clause
- pay attention to the logic
then you might not only figure this out yourself, but also you will get better answers.
Now, I find that the confusion -- not just yours, but mine too -- is the word family tree of to be and to become and then the subjunctification of it.
- sein vs. werden
- ich bin vs. ich werde
- ich war vs. ich wurde
- ich wäre vs. ich würde
werden is really not just a future form of sein. In German we don't even have future form!
All future is formed with "werden". Compare with Latin languages where you have a real future (such as in Spanish "comprar" - "yo compro" - "yo compraré") and then a future formed with the auxiliary verb "to go" ("yo voy (a) comprar"), like in English "I'm going to buy" vs. "I will buy". German and English also has no future form of a verb. And "werden" is not a future form of "sein". It is rather a "continuous" form of sein, as in progressively becoming. And in English "to become" is not a future of "to be". In German it gets murky because "werden" seems so directly related to "sein" because of "sein's" simple past "war".
Now I give you some real German that you can hear people say all the time to contrast:
"Ich wäre mir da nicht so sicher." - from "Ich bin mir sicher" - the reason I need the negation and the "da" is because you hear this in the negative, and "da" is pointing at the situation in which I imagining myself would I not be so sure.
"Ich würde das so sagen." - from "Ich sage das so" - "Ich werde das so sagen."
So, "wäre" you can only use in adjective assignments or in passive voice verb constructs.
But "würde" you use in active verb constructs.
This is how I explain this phenomenon to me.