Hi GD - I know this is awkward, and as the daughter of a woman who's been married 5 times (yes, 5), here's some input.
I think it's fine that she sit with your dad - everyone that knows YOU knows that she is the new wife and not your mom. Seating arrangements don't make her a mom, but having your dad's wife sit with him will make things nicer all around.
It's totally normal to feel irritated - especially now - because you don't have a real relationship with her, but you're both going to have to find a way to relate, especially if you have a good relationship with your dad. She's in an awkward place because she's "officially" part of the family through marriage, but NOT through relationship or affection - and that's the sticking part for you. When it comes to FAMILY - sometimes you have to find a way to include people and the including is not an HONOR but a DUTY (believe me, I know - I had to have my soon-to-be-SIL in my wedding because I HAD to, not because I wanted to).
You said she didn't show interest in you till the engagement - that's not really surprising because you had & have your own adult life apart from your dad when she came into his life. I's possible she doesn't know quite where she fits and quite how to handle how much to be involved, etc. I think your DAD's dropping the ball here, cause HE should be inviting you to family things and not expecting his new wife to muddle through his/her new family relationships without help/support.
Weddings get most girls excited so she wants to be part of it. If you don't have hard feelings about her - just ambivalent or you're unsure how she fits into your life, I'd find small ways to involve her & her kids that aren't directly wedding-party involved. They can feel a part, but don't have to buy any new anything, etc., and you can let them know that - ("Oh, dads-wife, we would totally love for X and Y to hand out programs. No need to worry about buying any special clothes - it would just be lovely if they could participate." Same for her - see where you could use her, what she'd enjoy, and then get a little gift for her and her kiddos (flowers, necklace, etc- nothing to break the bank, but a token of family). And have YOUR DAD step up to the plate a little here and help you help them feel involved. He's the one who got married, so HE should help build the relationships.
Your relationship will NOT be the traditional mother/daughter-in-law situation because of the smaller age difference. She is more of a peer than a parent figure. She'll have to accept that. Who knows, you may end up with a great friendship out of this. My stepsister - who is old enough to be my mother - is one of my best friends and has become a mother figure in my life.
I hope you find a richer relationship here than you expect. Don't worry about 20 years down the road. Just enjoy your planning, hold your DAD accountable to help with the relationship-building, be pleasant to his new wife, and have a fantastic wedding :)