It seems that you're looking at the work that words inside the phrase are doing, when you should be looking at the work that the phrase does.
Inside the phrase "green chairs that I have never seen before", a lot of work gets done. The adjective "green" modifies "chairs". The relative clause "that I have never seen before" modifies chairs. You're looking at the work that happens inside the phrase. Also, every word inside the relative clause is doing its own job. All of those jobs are filled inside this phrase. We don't have to worry at all about those jobs.
What about the work that happens outside the phrase? What kinds of things can the phrase "green chairs that I have never seen before" do?
Well, it can act as a subject, an object or a complement. "Green chairs that I have never seen before suddenly appeared". "Yesterday I saw green chairs that I have never seen before." "Those are green chairs that I have never seen before."
The work that is done outside of the phrase, the work that is done by the phrase as a whole, is the work that is done by the word "chairs". "Chairs suddenly appeared." "Yesterday I saw chairs." "Those are chairs."
Ask yourself two questions: What job does this whole phrase do? Is there one keyword that carries this job? For this phrase, the job that it does is the job of a noun, and the keyword that carries that job is the noun "chairs". The entire thing is a noun phrase.
Sure, "green" is an adjective. Please note that, if you're looking at only this phrase, that word's job is done. "Green" already modifies "chairs". Sure, the relative clause is an adjectival clause. Again, that job is already finished inside of the phrase. If we're looking at only this phrase, then the job that "chairs" can do hasn't been done yet. We need to put this phrase into a clause before we can see the phrase doing any work.
Same thing with "tall trees". The job of "tall" is done -- it's already modifying "trees". The job of "trees" isn't done, and won't be done until we can relate this phrase to some other words.
Same thing again with "totally unacceptable". The "totally" modifies the "unacceptable", but the whole phrase is still looking to do the same job that the word "unacceptable" could do by itself. "Totally unacceptable" is looking for some noun or noun-like thing to modify.
On its own, "totally" is an adverb. It's looking for some not-like-a-noun thing to modify. On its own, "unacceptable" is an adjective. It's looking for some noun-like thing to modify. On its own, "chairs" is a noun. It's looking for work as a subject, an object or a complement.
As a phrase, "totally unacceptable" is an adjective. The whole phrase is looking for the same noun-like thing that just "unacceptable" wants. As a phrase, "totally unacceptable chairs" is looking for the same kind of job that just "chairs" wants to have. In the sentence "Those are totally unacceptable chairs", the pronoun "those" is the subject, the verb "are" is of course the verb, and the noun phrase "totally unacceptable chairs" is the subject complement. Every word and every coherent group of words is doing the kind of job that it wants to do.
That should help you with noun phrases, verb phrases, adjective phrases and adverb phrases. Prepositional phrases are a special case. There exist both adjectival prepositional phrases and adverbial prepositional phrases.
For example, "the cat in the hat" is a noun phrase that contains an adjectival prepositional phrase. The exact same phrase can be adverbial in another sentence, such as "The money was dropped in the hat." On its own, "in the hat" is ready to do either kind of work.
Then again, prepositional phrases are easy to spot. They start with a preposition, and the rest of the phrase is the preposition's object.