TheRealThursdayNext YANBU.
You have a perfect right not to go to the wedding. I can see you are very hurt your sister has not talked to you about the fact she invited your father.
Of course it is her wedding and she can invite whoever she wants to.
Clearly you thought she would either not have invited him or would have discussed it with you.
It is not clear from your post how close you and your sister are. So I am not sure how relevant all the images of sisterly love are!
I do wonder if there is any 'issue' in the fact your father is in contact with your sister and not with you.
Having said all this, and really wanting to send some support to you in a rather 'hostile' environment, I would say that if I were in your shoes I would explore (mentally, I mean) whether I was prepared to go!
No one can tell you to go but by the same token I would not give your sister any ultimatums. When you need to made the decision, however close to the wedding, I would find out if your father will go and then make your decision based on this - and how you feel at the time, which may be different to now.
In your shoes I think I would get some counselling in the coming months to ensure that all the past was really behind me, including any hurt you may feel (sorry if I am projecting in here but that is what I wonder) about your sister having made a relationship with your father.
In your shoes, if I went, I would not take my kids, assuming there is someone who can look after them for the day. Whether or not I took my dh would be something I considered. I'd make sure my sister knew how many were coming so she did not cater for the whole family if they were not coming (that's the practical administrator in me!).
I'd go to support my mum, if she attends, as well as to be with my sister on her day. I'd asked to be seated next to my mum. I'd stay as long as I wanted to or as long as my mum wanted to.
I would not worry about wider family or what they thought or did not think.
I'd tell my sister if I was not willing to be photographed with my father and if there was a mix up and such a photo was called I'd head for the loo.
I am aware I am in the minority and I am not speaking from personal experience. At my wedding the photographer commented something like he could not remember the last time he had married a couple where both sets of parents were still married to the original spouse! Between my parents, parents-in-law and sister-in-law they had over 100 years of married life! BUT just because I have not been there doesn't mean that I can't see it from your perspective or have an opinion.
I do think someone made a very valid point about repercussions. There might be some. You are responsible for your own actions so don't mess your sister around or make her choose, just IMHO.
She's already had one wedding which you attended and your father did not. A lot of people miss weddings for ill health and I am guessing missed flights or all manner of things. Some weddings miss their guest as couples elope or go somewhere exotic and so pricey no one can follow! It is not such a massive deal IMVHO but it may be to your sister so you do need to know how she feels as well as how you feel.
Your sister's big day is about her marrying her beloved, not about exactly how many family members are or are not there. I would have been very sad if my sister was not at my wedding and you do need to think about your relationship with your sister in a calm way. Because I do agree you may be cutting off your nose in a sense and missing her big day because of the presence of your father, and you may regret it.
When all is said and done a wedding is not such a big deal IMHO, it is just a day, and relationships are what really count. So no one should be making anyone stay away but equally no one should be making anyone attend!
All the very best for whatever you decide to do.