It is a different sentence, but to an English-speaking learner, either outcome is possible. Word order, and the implications of it, is an on-going puzzle to many of us.
In this sentence [we want]+[something]+[to change] makes "we want something to change" look correct, but it is not. Usually, and certainly where a direct translation would not exactly make sense, swapping the order around arrives at a correct interpretation of meaning, but here it does not LOOK as if that trick is needed, and literal translation creates a wrong meaning.
So, how DO you express "we want something to change". simply. Can it be done with these same words differently arranged or with some simple addition or adjustment, i.e. without introducing additional or alternative verbs?
But what what does "We want something to change" mean? If it means that you want that something change (by itself), then it would be "Chcemy, żeby coś się zmienło". If it means that you want something so that you could change it, in other words you want to change something, then it would be "Chcemy coś zmienić". It seems that it could also mean that you want something to change something else and not that "something" which is mentioned in the sentence - "We want something in order to change (something else)". Although it may sound far-fetched without some proper context. If so, then it would probably be "Chcemy czegoś do zmiany/zamiany"/"Chcemy czegoś, aby zmienić ..." or similarly.
I was more mainly trying to point out at the literal meaning of the sentence, but I can imagine it being used as an equivalent of Polish „Chcemy coś zmienić”. Languages are alive, they don't need to follow cold logic all the time. The speakers using that phrase in English could in fact mean that they want to change something themselves.
Again, this might not necessarily be a standard way to translate Polish „Chcemy coś zmienić” nor would Polish use „Chcemy, by coś się zmieniło” in that context. I agree that it should not be accepted, lest the learners won't correctly memorize the real meaning of words and that in this Polish sentence the subject is „my”, not „coś”.
EDIT: Although now that I think of it, it could have been the result of incorrect word-by-word translation rather than conscious alternative phrasing.
My impulse was to translate as Machaljean did and I wrote "We want something to change". I had a nagging feeling that it would be wrong. I can understand the nuance, but to new learners, the polish construction is, in my opinion, close to how one may think in English. I have to force myself to mentally move nouns and pronouns before verbs to sound (and think) more "Polish". I say all this to offer that perhaps in the new tree there can either be exercises in helping learners develop this shift in thinking or some kind of pop up with a tip or example of how this would be in Polish. Like, "remember that the noun comes before the verb in this example"?
This is pretty much how perfective verbs are created in Polish. By adding a prefix to the basic verb you make it perfective, with different prefixes having different meanings. The Uncyclopedia explains this humorously on the example of verb „lecieć” – http://uncyclopedia.wikia.com/wiki/Polish_language#Verb_prefixes
Just don't read too much into the rest of the article, it's intentionally incorrect for the sake of humor.
Sometimes you can make this new perfective verb back into imperfective by changing the suffix.
va-diim is right. If the subject of the wanted action is different than the subject that wants it, then you have to make it a subordinate clause starting with „żeby”. So if you want to say "We want something to change" you would say „Chcemy, żeby coś się zmieniło”.
As you can see, we also added „się”, because the changing is performed by the subject on itself. And we now also conjugate the second verb, instead of using the infinitive form, since these are separate clauses now.