You didn't ask me but, as I'm sure must be the case with any language, there are lots of different ways to say basically the same thing in English, none of which are "incorrect."
A certain amount of deviation from the "formal" rules of language is prevalent in spoken language, completely aside from differences in dialect, etc., also. Many more things are left implied, rather than explicitly stated, in spoken language. As long as people can understand what you mean, no one really cares about strictly following the rules.
I'm sure this makes it more difficult for people to learn a new language, especially from books, from afar.
BTW, should it be "on the way from work" or "on the way home from work"?
Here throwing in "home" would be "correct" but leaving it out wouldn't be any major breach or make the sentence incoherent. Maybe "home" would be wrong, actually, because you're not going home, but rather to your brother's. You have not said, exactly, if you omit your ultimate destination. But it's not important to the meaning, so no one would really care.