She has shown a rather clumsy attempt to include you in the later meal out with the two of you alone but I wonder why this second venue could not be the place where all her friends could have lunch.
It seems to me she really does not understand how hurtful she has been to you, so no, you have not reacted 'over the top' to her proposal- especially as you have supported her through her family issues in the past.
You could kill her with kindness-tell her you would love to toast her birthday with a bottle of bubbly you pay for prior to the actual meal at the restaurant where they are going for lunch-that might give her pause for thought!
You could further go away after the toast and come back with a beautiful GF birthday cake after the meal if you really wanted to turn the screw.
Or you could just quietly drop this person as a 'friend' and always be too busy to meet up in future?