Food for thought- if you don't go then that will be the end of your relationship (and any chance at a future relationship) with your sister and your Dad with his daughter.

Or just maybe the wedding is about the bride and groom. Just because someone is blood related doesn't give them priority over those that aren't. I don't think that your family should be expecting to be highly involved in the wedding, if you guys haven't be highly involved in her life (regardless of who's fault that is). If you are going to get your nose out of joint over a seating plan then don't go because your family isn't going to be able to handle her Step dad walking her down the aisle, making a speech and having the father/ daughter dance.

Assume the best but prepare for the worst. If it is an olive branch, it would be a huge snub not to go. I would go with the intention of just being a general guest, not expecting to be seated at the family table, just there to support her if necessary and to enjoy the occasion with your parents. Withhold the present and card to drop off later in case you kick yourself for spending it on the day. If things go pear shaped you can always just leave knowing that a huge expense was paid to get you there and you haven’t wasted any $ on them yet. If it has been done with good intentions, it will be a great start to a better relationship. Good luck.

I invited my parents
My brother and his kids
My sister and her husband
That’s all the family I invited cause most of my aunts and uncles are idiots

Hahaha really? She's petty enough to make a whiney little bitch point on her wedding day? "This is one of the best days of my life, time to stick it to the man" 😂
Tell your parents what you know. Discuss with them your concerns and make a group decision to go or not. If you're worried about looking petty, just don't offer a reason for not attending. Or if you decide to only go to the service say "look, we know that this is an important day for you. We'll stay for the ceremony and you can enjoy the reception with your friends".
At my wedding my stepdad was very gracious in his approach to it. He made it explicitly clear that he was just another guest (despite him paying for the whole thing!) and that my father was to do all of the dad jobs, regardless of whether he was there for me most of the time growing up or not. It really made me love and respect him more. He raised me mostly. He was the one who took me for my first driving lesson, he was the one in tears at my high school formal, he was the one who put up with my bratty teenage years and awkward preteens. My own dad was often times too busy or too high to do that (I still absolutely adore my real father though).
I'll never forget the grace and diplomacy my stepdad employed at my wedding. My first son was actually partly named after him. Maybe your dad will take the same route and your sister will realise what a great man he is.

My step mother only invited me and my siblings to our Dads 60th so she could rub it in our faces how much we don't exist to them. I knew it was going to be like that so I didn't go but my brother went and had to sit through a slideshow which showed photos of my Dads life and everyone in it except for the kids from his first marriage, a whole 15 years of his life cut from the slideshow. They had plenty of photos to use but didn't. My younger half siblings made speeches while my brother was not asked if he wanted to add anything. He was completely ignored the whole night by my step mum and Dad even though he had travelled interstate for it. Luckily my uncle and aunty stayed with him all night, they could see what was going on so they just sat there in the corner drinking all the alcohol making jokes about everything. He regretted going, he felt like it was only to somehow punish him and show him how little he meant while my Dads new family meant the world. If she is only inviting you all so your Dad has to sit there and watch someone else play father of the bride then it will not be an olive branch. If she hasn't made an effort to be friendly when you've tried before then I doubt she is going to change anytime soon.

This is tricky. My first thought is: It's a friend of a friend. How much can you trust this information? It just seems a bit strange to me that your sister would invite you to her wedding with the sole purpose of humilating your parents. Why waste the energy and risk looking petty on your wedding day?
On the other hand, people can do some strange things. You have seen the screenshots, I think that you need to go with your gut on this and talk to your parents. See what they think. The trouble is if go, your parents could be humilated, if you don't then it will be; they didn't care enough to come to my wedding/reception.