Well, ftg, I could have sworn that they carried the baby out the trailer door and down to a picnic table in their front yard, which would seem to indicate that they were just cooking out at the trailer. Previous shots of Ed and Hi outside show the trailer as being pretty much out in the middle of nowhere, so it seems reasonable that Hi and Glen were walking around near the house rather than walking through a park.
As for the background looking like a particular place, well, it might very well have been filmed there. That doesn’t mean that the story was meant to take place there, though. Only people familiar with the areas in question would know the difference, and they make up a tiny portion of the total audience. It’s like in Seabiscuit when they’re showing races at Pimlico. Those scenes weren’t shot at Pimlico, but rather at Keeneland. People who are familiar with either track would know the difference, but the rest of the world not so much.