I wouldn't be bothered if an eight year old was too homesick to sleep over at my house. She's only eight, for crying out loud. There could be a THOUSAND reasons why she prefers to stay/play at her house, so why assume the worst? Sometimes in life and in friendships, you simply have to take people as they are. And if you don't like how they are, you have to move on. You should always try to give people the benefit of the doubt, though, and not assume there is some malicious intent on their part (unless it's undeniable).
I honestly don't see why it was so nervy of them to ask you to bring dinner over to their place (especially since it's only twelve paces away). If I had just purchased a new dog, I wouldn't want to leave it alone for a while until I was certain it wouldn't tear my house to pieces while I was gone.
But look, for whatever reason, these people rub you the wrong way. So you have two choices, you can exercise some tolerance and get over your frustrations...or you can cool your friendship off and maintain a civil acquaintance. Either option is perfectly acceptable.
But as far as your daughter's friendship, I wouldn't interfere. Tell her to be honest but try to spare the other person's feelings as much as possible. A good life lesson for sure.