I think it is a fair request, if a bit rudely worded on the invitation. We had no free bar at our wedding and no-body seemed to mind this, although they got their meal paid for.

As for the reception only invite, tbh I am a little shocked that so many people seem to think this is out of order. It is commonplace in the UK to have a larger reception than wedding, although usually the wedding and meal are one thing, and then more people come for the evening dance. So to get a wedding reception invitation would raise no eyebrows. IMHO a wedding is a serious and solemn set of vows between two people in front of their closest supporters, which is then celebrated by all and sundry (if they choose).

I would call the bride and just ask about the meal, costs, etc. Also ask about the kids. If they were not mentioned on the invitation I don't think you can take it that they are invited.