Well, we could accomodate most of your requests. My dad has a house for rent in the area. It is 4 bedroom, 2 bath, 2557 square ft. It is new construction and has never been lived in. It is in Green Cove Springs so it isn't exactly "close" to base, but we live nearby and think that it is certainly worth the drive (30 min.) Particularly because the schools are so much better and the neighborhood is wonderful. There is a community pool just finishing construction about 4 houses down. Also, quite a few military families live in the area and there is a huge park across the street from the subdivision.
Finally, I spoke with my dad and asked him how he felt about the Golden and the cat. He said that he would have no problem allowing you to have the pets so long as you would be willing to provide a non-refundable pet deposit.
Feel free to e-mail me if you have any questions or if you would like to come and see it. It really is a beautiful home.