The requirements do not demand an open-water swim, though that's implied. The requirements do not demand a child use a certain stroke. The requirements also don't explicitly demand that the mile swim be continuous. So everything we see here, including doing the swim in stages, meets the letter of the requirements. So, yes, if a lap pool swim is okay with the aquatics counselor, then it's okay.
Yes, there's a difference between swimming a mile in a pool versus swimming a mile in open water. But there is a far bigger difference between swimming a mile freestyle versus swimming a mile using
