some troubles with passsives

Actually, a pedant would insist on A as the "correct" rendering, since B ends with a preposition, which is (according to the language pedants) grammatically incorrect.

I'd agree, although for different reasons. A sounds perfectly fine to me (and is perfectly acceptable English), where B sounds more stilted and ugly to my ears.

I agree that Dave made the better choice of the two options given. However, there's a third, more complete option.

It's really easy to "lose" pieces of the active sentence when converting to passive, and vice versa. Let's use as an illustration another active sentence similar to your sample sentence:

"Santa Ana's forces gave no quarter to the defenders of the Alamo."

If I was to formulate an "A" and "B" sentence like yours from the example, this is what I'd get:

A) No quarter was given to the defenders of the Alamo.
B) The defenders of the Alamo were given no quarter.

What happened to Santa Ana's forces? (Well, they defeated the defenders of the Alamo, which gave rise to the rallying cry of Texan independence, "Remember the Alamo," but that's a story for another time, kids.)

The passive sentence that truly corresponds with the example would be, "No quarter was given by Santa Ana's forces to the defenders of the Alamo."

Therefore, the passive sentence that corresponds to your example sentence would be more like, "No notice was taken by them of her rude remarks."

You may also choose to simply flip prepositional phrases around in either example I just gave, which would yield:

"The defenders of the Alamo were given no quarter by Santa Ana's forces," and

"Her rude remarks were taken no notice of by them."

I'll throw in another voice for A, though I'd replace B with "Her rude comments were ignored".

Mmm, I think A sounds much better.

Choice B is completely incorrect not only because it ends with a preposition but also because "her rude remarks" was not the direct object of the orignal sentence. Rather, it was the object of the preposition "of."

"Notice" was the original object of "took," therefore, it is rightfully the subject of the passive version "was taken."

I object to the word 'better', without an explanation of what this 'better' might be. Better for whom? Better grammatically? Better historically? May be I am dense, as I am not a native English speaking person, but your question sounds very ambiguous in my ears.

Although Marta didn't directly state her idea of what "better" means, she did say that she's trying to find the one that "sound[s] natural" and is grammatically correct.

Coming from an Iowan point of view, I think A sounds much better. I don't think I've ever heard anything like B before.

Hear ye, hear ye.

It hasn't been "completely incorrect" to end a sentence with a preposition since, oh, people stopped speaking actual Latin in colleges.

Come to think of it, it's never been incorrect to end an English sentence with a preposition. Some Victorian busybodies noticed it never happened in Latin, so OBVIOUSLY that meant it should never happen in English.

After all, Latin and English are the same language, right?

Not.

I would say "Her rude remarks were ignored"

I have to agree with Caitlyn here. Simplified, the original sentence boils down to "They took notice". The passive form would be "Notice was taken". I don't think anything that doesn't derive from that works in this case.