Visiting other resorts is certanly allowed and resort hopping is one of my favorite things to do at WDW. The amenities; pools, gyms etc are just for the guest of the hotels. That being said, I have never seen a playground at a resort very busy and asking nicely at the counter might get you an ok. I have never been very impressed however with the playgrounds at WDW. Not really very special. DS did play at the playground at FW once while waiting for HDDR. All the kids waiting were playing there.
Jordans' mom