Outdoor Birthday Party Venue That Allows Petting Zoo/Pony Rides

Hi, 

I'm currently trying to plan out a Moana-themed birthday party for my daughter who is turning 4 this upcoming April. We have booked an indoor venue for the Friday before her birthday and are looking for an alternative outdoor venue in East Bay for the following Saturday. Initially, we were pretty set on Roberts Recreational Park since it's less than 10 minutes away from home and would make it much easier to do multiple trips back and forth to lug around party essentials.

However, there are a few small details that I think could affect the enjoyability (I checked, it's apparently a word) of the party if we decided on Roberts:

• The playground is about 50 feet away from the picnic tables, which means it'll be harder to keep the group together and have the parents sit/relax/eat during the party.
• They don't allow mobile petting zoos or pony rides. While this wasn't originally part of the plan, we found a company that offers a petting zoo, pony rides, AND balloon twisting for an hour at the relatively low price of $250.
• There is no canopy/covering available.

Would those of you with far more experience throwing kids birthday parties around the Bay Area have any alternative suggestions? A friend of mine suggested Mosswood, but unfortunately they recently experienced extensive damage due to a fire back in November.