Proceed as planned. That is life, you're not always going to get invited to functions, and you'll just have to learn to deal with it, so better to start learning at a young age. I have good friends who are religious, I am not, so they don't invite me to their religious functions. We see each other practically every weekend or talk to each other on the phone, but they know it might be awkward for me to be in a church. They will send me pictures of things like their confirmation, but not invite me. I am not upset or hurt, I would not invite them to functions where there are people who are vocally against religion because it would be offensive, and they don't invite me to religious functions where I may be preached to or told I am going to hell for not going to church.
Same with music, if I know someone's musical taste varies from mine, I won't invite them to the types of concerts I attend. I also have married friends who have double dates with other married couples, I am single, so I am not expecting to be invited and play the part of the third wheel. They have more sense than to talk about it, or they will briefly mention that they went to some restaurant and loved it, as if to recommend trying that joint, but don't rub it in my face and bring up what a great time they had with the others constantly, as if to make me uncomfortable or resent the fact I am single. Like I said, it is life, not everyone feels comfortable with situations or attendees at a party, and not everyone has the budget to invite more than a small gathering of close friends, as is your case. We all learn to deal with it and get over it. I'm sure the neighbor girl doesn't feel your daughter is her BFF and will start crying over not being invited...