That is super cute! Is the blue part a pencil protector case? The type that fasten into a notebook? It looks like that size. You fastened it with zip ties?
As for the main question, I'm with the group: I'd leave diapers, wipes, drinks, sunscreen, etc. in the storage area /covered by a blanket ... but not valuables. I wouldn't carry a wallet into the parks ... just a couple dollars and a credit card in my pocket. Sometimes I carry a phone, sometimes I carry a small camera ... with the baby, we'll definitely take a camera. We don't buy souvenirs , so no problem with that.
On our next trip we'll have a baby and will want to bring snacks ... have not considered squirrels. Would a heavy-plastic container deter them, or should I look for an old metal lunchbox on ebay?
You've heard the term: crimes of opportunity.