Yes, that's correct. Is refers to the subject, so mi has to be present. Is can't belong to an omitted word.
But if is belongs to a verb with a prefix, it separates them: oda is sietünk. And yes, it can also mean that we do not only hurry here, but there too.
The only case where people might put is after a verb with a prefix instead of separating them is when a clause starts with ha or még ha:
- "(Még) ha elmegyünk is az orvoshoz..." -- "Even if we go to the doctor..."
But you can put is between the prefix and the verb here too, and, while I'm not sure about the rule here, I prefer it that way:
- "(Még) ha el is megyünk az orvoshoz..."
Yes, this "even if" kind of usage of "is" is kind of weird. I suspect that it is a contracted version of a more "regular" structure:
"Még akkor is, ha elmegyünk az orvoshoz...."
Very literally: "Even then, too, if we go to the doctor..."
And this gets shortened to either one of these:
"Még ha el is megyünk az orvoshoz..."
"Még ha elmegyünk is az orvoshoz..."
So, "akkor" (then) gets dropped, and "is" finds a new host.
The difference between "elmegyünk is" and "el is megyünk" is very very minimal at best.