Originally Posted by Madhava
You could use either:
In 1. above, you use the present progressive tense twice, and thus it has the ring of redundancy, since the present progressive is already implied by the phrase "As we were driving ...". Such redundancy would not be considered wrong -- if the speaker or writer wished to emphasize the present progressive act of "going past some dogs".
- As we were driving around the park, we were going past some dogs.
- As we were driving around the park, we drove past them (some dogs).
Without such intended emphasis, you would be more apt to hear #2. above.
You might also consider:
As we were driving around the park, we past them (the dogs).Here, you also get rid of the redundant "driving ... drove ..."
One further construction for consideration:
As we past them, we continued driving around the park.