I think I see why you could argue the script needs to include the party this woman isn't invited to- to get across that the last gathering didn't work for the host, and she therefore intends to hold only dog-inclusive dinner parties and not to invite this person because of the discomfort everybody experienced this time. If she is willing to do other things with this friend instead, then I think she should invite her first, and explain this non-invite situation afterwards (assuming the idea is to be honest to avoid dog-hater hearing of the party through mutual friends. If that isn't true, telling her about it comes off awkward and weird, but if she is explaining to avoid awkwardness that is otherwise likely, it's understandable). I definitely do not think she should start the conversation with "I'm having a party but you can't come".