Do they have a doggie facility at the park

Nopw

I didn't see any place there but I would contact guest services.

PET KENNEL Pets are not permitted in the park, with the exception of service animals. Although you can’t bring your four-legged family members into the park with you, we do offer a convenient pet kennel. It is located right in the main parking lot and you can board your pet free of charge! While you are inside the park, DO NOT leave your pet in or tied to an unattended vehicle. Los Angeles County requires proof of rabies vaccination in order to board your pet, so be sure to bring all documentation with you to the park.

Yes they have a place to leave your doggie or even places for them to have their release inside the park