Why would Pink Sis even bother wanting to send flowers ( joint gift or not) - does she think that you don't talk to her as well ?? It may well be that they will never see eye to eye but expecting you to chose one or the other is naive and immature.
As BM says - honesty is the best policy here. Tell Pink Sis you have been invited to the party and will be going and you assume she has not had an invite due to them not talking - if Pink Sis wants to sort it out with Big Sis that is their business.
This cloak and dagger stuff and trying to remember what you said and to who will inevitably fail. Which will then make you the focus of the 'betrayal' and the anger magnet.
I have 2 brothers - they are both very different. But my brothers don't really speak to each other - this is since my mum's funeral and issues with their respective partners. These are their issues though and not mine. They both know I am keep in contact and see them both but when they ask about the other I refuse to act as any sort of intermediary . They are grown ups allegedly