Honestly, your sister sounds like a bully. Yeah, it's possible she sees your response as a slight on your relationship, but it's more likely that she knows that family togetherness is your weak spot, so she dove right for it to try to guilt you into changing your mind. You need a consistent, calm response that you whip out every time she pulls this, along the lines of, "gee, I'd love to spend time with you, but that's not in my budget. Can we have dinner at my place instead?" [Or insert some other free/cheap get-together] If she really is clueless, repeatedly offering her a simpler alternative will emphasize that you do want to get together; if she's just using it as a guilt trip to bend you to her will, the consistent response will eventually persuade her that you are done being a pushover.
Also, expect it to get worse before it gets better -- people who are used to getting their way will tend to get even more aggressive the first time you say no, because they are used to you giving in, so they just assume if they push harder, you will resume your rightful (submissive) role. Kind of like kids and tantrums, btw -- this is basically an adult tantrum, and so treating it as such tends to work very well. FWIW, remaining calm and saying the same thing over and over will drive this kind of personality nuts more quickly than anything else -- first you're not doing what she wants, and now she can't even get you upset or angry or guilty about it? It just sucks all of her power away from her, if she is so insignificant that she can't even ruffle your feathers.
And, yeah, I do have one of these. I still remember when my SIL invited us and her other sister out to a very fancy restaurant (one of those with a famous-name chef) to celebrate her birthday. DH and I were just married and had just bought a townhouse, so I was worried at the cost, but the SIL had introduced us and was clearly excited to have me in the family and wanted to include me, so I put my hesitations aside and went. And boy had she set this up -- she had gotten the chef's table and set up this fantastic menu (e.g., we were greeted with the largest tray of charcuterie I have ever seen), which was definitely delicious, but waaaaay more food than we could possibly eat, and of course paired bottles of wine with each course. And then she presented us with the tab. For like $800*. Because after all it was her birthday.
WTF? Who does that? If she'd asked if I wanted to take her out for her birthday, I'd have said of course, and chosen a reasonable restaurant -- or at a bare minimum, taken over the planning to keep the menu and wine reasonable (we could easily have eaten at the same restaurant for less than half that cost). But being presented with the check at the end was a real dick move that left us feeling like we had to pay to preserve family harmony. And it was delicious, but not $400 delicious. I really felt bad for her other sister, though, who made a lot less than the rest of us at the time -- I mean, you just don't do that, period, but you sure as hell don't do that to people who make maybe half of what you do. Lucky for me, SIL was just clueless, not mean-spirited, and she's changed her ways since then.
*Note that this was 20 years ago. By today's inflated dining-out standards, it would probably have exceeded $2K.