Take a bus and/or drive to the ticket and transportation center and hop the monorail to the polynesian or scheduling a dining reservation at one of the poly's restaurants should make that happen. As long as the pool isn't approaching capacity, I haven't seen them check room keys to make sure you're staying at that resort.
As far as kids are concerned, it surprises me that that would be their pick. It never really struck me as appealing to kids but who knows maybe I'm crazy. The Beach Club and/or BLT's pool seems much cooler. And the Kidani pool area looks very nice.