One thing is the tickets. A two year old gets in the park for free, so she won't have the same ticket as a 3 year old child would have, they will know she is only 2.
I suppose you could go ahead and buy her a park ticket as if she had already turned 3. Really that would be lying about her age though. But if you don't mind giving up the "two year olds get into parks free" thing, you could purchase a park ticket the same as what you purchased for your older daughter, and then everybody would think she IS three years old. I wouldn't do it because first of all it isn't honest and secondly there are concerns about the makeup being on a child under three for safety so I wouldn't risk it.
Part of the benefit of being 2 is you get into the parks free, but, that comes at a price because you're not allowed to participate in everything.
They are VERY strict on age limits and will NOT let a 2 year old participate. Many people have tried, but they always get the same answer.
I think you have three options:
1, don't take her at all, and tell her that's it's a special thing that she will get to do when she is older like her big sis and she can look forward to the day when she is old enough to go,
2, buy her a park ticket as if she is already 3
3, If you want to give her a nice experience but not have to lie about age, you can just take her to mickeys barbershop to get her hair done (they take babies) and bring a special dress you can give her to wear so that she can be a Princess too.