Yeah, I do like being in an all-hugs-all-the-time environment.
So here's an update:
A week or two ago we were on our way somewhere and the sozlet saw Jack and Emily playing and wanted to go play with them. I took a deep breath and said, "Sure!", and we went over there. When we got within range I said, "I hope we're not intruding..." and Emily's mom said "Oh no no of course not come on over" and Jack's dad kinda waved. (Jack's dad is a stay-at-home dad, which I think is cool.) So we hung out for a while, the sozlet had a blast, Jack and Emily seemed to enjoy playing with her. But I was still a little hesitant -- Jack's dad and Emily's mom seemed to be having a big conversation when I arrived, and he excused himself in fairly short order (to check on the baby, though, which made sense) and Emily's mom asked what time it was after a bit and said that she had to go pick up the older kids. So it was totally nice and fine and we had a good time chatting, and I didn't feel like I was getting the bum's rush at all, but I was still just a bit uneasy.
So earlier tonight the sozlet and I were sitting on the front porch, and Jack's mom was taking out the garbage. She saw us, I waved, she waved, and then she came over! FINALLY! This is the first time anyone has crossed the street in our direction, I think. She was really really nice and said, "I saw you and [the sozlet] playing by yourselves in your yard the other day when we were out -- if we're out, COME OVER! <I demurred a bit> No no COME OVER already! Don't worry about it! We'd love to see you!" She was QUITE emphatic about it, so I now feel much better and plan to take her at her word.