I have never heard of a destination birthday party. Wedding, yes.
Be that as it may, I Googled the term and, unfortunately, you're not alone. And I say unfortunately
because I find this to be nuts. I like vacations as much as anyone else, but to have them dictated by my friends - and more than once? Yeah, not so great.
So! Here's the deal.
She is turning 52 and not 55 or 50. So it's not a big deal oh my God I can't believe I made it to ____
sort of a birthday. I take it she has not been diagnosed with 6 months to live, either.
Hence pick one of the events, either the 4 hour away deal or the dinner, and tell her you can only attend one. You're watching your kids' soccer game. You're taking your mother to look at cemetery plots. You're studying for a big test. You have to work for part of that weekend. Whatever. But the truth is, you don't need any sort of an excuse. Just say you can only go to one. If pressed, just say, "I've got plans!"
She doesn't know you're going to binge-watch 8 seasons of Doctor Who
, or whatever.
As for a gift, make it small. She's in her 50s. She can buy her own clothes, etc. So bring a small bouquet if that's appropriate or buy her a small nice piece of costume jewelry, or just give her an envelope and, inside it, put a certificate for a free dinner and time spent with you. And call it a day.