We are from out of town and staying at the hotel. My cousin lives close by. Would it be a problem having her and her 2 children use the hotel pool/waterpark with us as our guests?

Talk to the front desk. They require a green wristband for use of the pool, but they might give extra if you ask. I did see them kick people out of the pool area because they didn't have wristbands, so it is inforced.

For us the only gave us one wristband per occupant of the room.

Yes you can the room comes with extra passes for the pool.