It's simply impossible to replicate everything you have at home at your destination. And it's unnecessary. Focus on the priorities. Start with what you'll need as soon as your plane lands and you leave the airport: car seats and a double stroller. In most cases, you'll want to bring these with you. Keeping the kids contained in their double stroller makes it much easier to transport them through the airport. If you've bought seats for the twins -- and possibly even if you didn't -- you will want the car seats for their comfort and safety during the flight.
Strollers
Strollers can usually be gate checked as you board your flight. This means that you can use it right up until you board the plane, and that it will be waiting for you as you leave the plane. However, policies vary from airline to airline and from flight to flight, so be sure to confirm with them. If you do have to check your stroller, ask the airline if it counts against your checked baggage tally to avoid paying excess charges. Also, package it securely to avoid damage. Consider investing in a sturdy bag or tote designed to protect it, or pack it up in a box. Make sure latches are secure so that it doesn't come open. If you have more than one stroller, choose your smallest, lightweight model.
Car Seats
If you're renting a car at your destination, it is likely that you can also rent car seats. Be wary however, and check out your options fully before you choose this path. Don't rely on what the national reservation service tells you; call the local rental office directly to ensure that they have TWO seats available, and that both seats are appropriate for your childrens' age and weight. I think it's wiser to simply bring the seats with you. Chances are you'll use them in-flight, and if not, you can always check them. Most airlines do not count car seats as part of your checked baggage, but confirm this policy to avoid excess baggage charges of $25 or more. If you check your seats, be sure that they are packed to avoid damage. You can buy car seat covers and totes to protect them.
Don't bring:
Plan to buy anything consumable or disposable at your destination: diapers, wipes, formulas, baby food, etc. Try to arrange to have someone at your destination purchase the necessary items so they're ready when you arrive. If these things simply aren't available where you're going, consider shipping a box of them prior to your departure so that they're waiting for you on arrival.
Do bring:
Next: What can we borrow/buy/rent when we arrive at our destination?
