The second sentence with its three parts is perfect, maybe a bit repetitive, but that can also be a rhetorical means of emphasizing, which seems to fit what you're saying.
In the first sentence, the position of zusammen that you chose sounds just a tiny bit off to me in more formal writing, while fine in everyday use, but I'm not even sure other native speakers will also see it that way.
I would probably put it before the immer or at the end of the sentence.
Wir machen zusammen immer viel Spaß.
Wir machen immer viel Spaß zusammen.
Zusammen machen wir immer viel Spaß.
Even though it's not the question, let me add that the idiom "Spaß machen" might not be what you're trying to say here. Well of course I don't know what you're really trying to say, so ignore this if I'm wrong...
"Wir machen Spaß" as it's used here, with a person or persons as a subject means something like we're (actively) joking, bantering, fooling around.
It's different from "Lesen macht (uns) Spaß" (with the person having fun being the object and the thing that is the actual fun being the subject, like "Reading is fun to us") or "wir haben Spaß" (we have fun), which could be what you mean here.