I think part of the problem here stems from how we translate things from Japanese. It seems that there is a strong preference when translating from Japanese to keep the voice of the verb: ie, whether it's active or passive. I don't agree with this for learners because it can lead to confusion. Consider the two sentences
Let's assume it's my mom who read a book to me. In this situation, they're both translated the same: "She read the book to me." But what's being lost in translation here is that the subjects of the verbs are different. In the first sentence, "mom" is the subject. In the second sentence, "I" am the subject. For the second sentence, we can preserve the subject in English but we can't do so without resorting to the passive voice (see below). If we don't leave anything unspoken in the Japanese for the scenario I'm describing, then the above two sentences become:
Both of these sentences are likely to be translated as
My mom read the book to me.
And, in fact, the first sentence is quite accurately translated as
My mom read the book to me.
But regarding the second sentence, this translation misleads a bit regarding the subject.
We could preserve the subject by being translated as
* I was read the book by my mom.
Granted, this is a rather awkward sounding sentence in English; also, there's nothing in the Japanese that is passive about the sentence. But as a stepping stone to grasping what's going on here, I think this approach can be rather beneficial to the language learner since otherwise the learner is left to wonder why there are two different verbs to express the very same idea--answer: because the verbs construe different subjects. That is, in Japanese, the subjects of the verbs are completely different.
So, in the sentences for your post
Though there's not enough information in the second sentence to really decide who is the recipient and who the giver of the benefit, let's just assume that the recipient of the favor in both sentences is "me". And, let's use "they" for party granting the favor (whether it's one or more individuals, may the traditionalist English grammarians not attack!). Both of these sentences could be translated as
They brought me along.
That translation works very well for the first sentence since it preserves both voice and subject. But in the second sentence, "I" am the one who receives the favor and it is "I" who is the subject. So, we could translate it a bit awkwardly as
I was brought along by them.
Or less awkwardly as
I got to go along with them
In both sentences, we preserve the subject. Unfortunately both English sentences are passive while the Japanese is active. Nevertheless, I hope this clarifies some of the differences going on here between てくれる and てもらう.