I agree about the geese at the park probably having been antagonized by kids. If you watch them, a lot of parents seem to think it a wonderful experience to let their children go out and chase the geese, or ducks or anything else that may be cruising nature. I'd develop a bad attitude too if I was being chased on a daily basis. My Chinese Gander is a doll. I give him his little "goosey" massage everytime I go out there. He is protecting the female right now who is sitting on a nest. But even then he just stands in between you and her and makes lots of noise. He might nibble at you pants or shoes.
As far as penning them together with Chickens, I read that geese are a good addition to a free roaming area because they will "guard" the flock whether it be intentional or not. Just their noisy and intimidating presence is a benefit to any other critter you got out there. My geese are indifferent to the chickens. The only time they pay attention to them is if someone comes out with treats. The chickens will run over to grab up treats while the geese noisily waddle on over, and upon their arrival will chase the chickens away.
The geese have their own pen for at night and the chickens have theirs. But I too tried to keep the geese out of the chickens. I put an 18" trellis in front of their pen. It worked for the geese. It was too tall and the geese were too big and awkward to try to go over it. However, it succeeded in keeping the chickens out too. These same birds that jump the 4 foot fence into my backyard and patio area seemed flustered and not able to figure out to jump over the trellis. At night, I kept finding them roosting on the stacks of bricks just outside the side of their pen. (Have you ever tried moving a dozen sleeping chickens? They don't wake up...Hilarious! My hubby compares it to moving the sleeping child from the couch.) So I put a cement block in front of their pen with the open sides up. Chickens did not seem too mind this one and easily hopped over it to get in and out. However, it only stopped my gander for about a week. Although clumsy, he gets past this new obstacle easily now. My female doesn't find it worth the while though and doesn't even attempt to get in there.