Anything's possible in shipping...especially if you have the right amt of $$. I'd think you could ship a keg in an igloo cooler packed with ice packs and taped shut. I say ice packs because they aren't as messy as ice, so no leakage. And I'd use the igloo max coolers so the keg would stay colder longer. Even the biggest cooler won't fit both kegs, so you'll need 2 of them. Looks like the maxcold 70 is your best bet. Going to take a TON of ice packs also.
Igloo MAXcool coolers: 2 @ $70
Ice packs: 50? @ $2
Shipping for 2 coolers: $$$$$
Having homebrew at your sisters wedding: Well.....expensive to say the least.
A full keg weighs 60lbs iirc. Say 10lbs for the cooler, and 30lbs for the ice packs. You're looking at 100lbs give or take. Shipping 12 states over, lets assume you live in Bangor Maine, and your sister is in Flagstaff Arizona. That's 12 states...depending on your route. So, we assume 200lbs via the cheapest service (UPS Ground). That's only $170+ for shipping. Or if you're feeling thrifty and send it late, you can get next day delivery for $800. Boy...what a bargain. Sounds like a road trip may be in order.