Also consider the practicalities of shipping plants on a plane, especially ones of non-trivial size, on an international flight. You have to count on them being "in transit" for a day or so, because you have to pack them in advance of your flight (and since this takes time to do right and you won't want to miss an international flight, at least several hours before, best the night before). If it's like coming from the US to Iceland, they'll have to be soilless, so you'll be coddling the roots quite a bit trying to make sure it's a gentle transition. You may tell yourself that you'll plan to just put them in a sterile potting mix in your suitcase but when it comes down to practicality, in most cases, you'll find that just wrapping well in damp paper towels / cloth / etc and then protecting with plastic is best. You're going to have to find luggage that fits them, difficult with trees. I modified a box for tube lights to fit the plane specs without going oversize (although I did have one bag go overweight). Even if you go oversize, you have to know that there are limitations on what they'll allow period even if you pay the extra fee. Trees that are too tall, you'll just have to prune or, as in the case of my mango and cherimoya, carefully bend (their tallest branches are still deformed, lol... it became permanent). If you're taking a number of plants, you're going to have to pack them in tightly. Expect some leaf damage from all of the sliding and squishing (might want to try to protect your leaves better than I did mine). You'll want to consider that it's cold at altitude, potentially even below freezing, and decide whether you want to just chance that or to take precautions. Insulating a box full of plants isn't as easy as it sounds. The best you'll probably be able to do is stuffing clothes into gaps, although you may decide that stuffing more plants into those gaps is a better plan
I used heat packs (and tons of them) to keep up the temperature, but therein lies another problem: heat packs don't last that long. So instead of following the instructions and removing the center part (a package of iron powder which rusts when exposed to air to release heat) from its oxygen-blocking plastic wrapper, I had success with simply making small pinpricks in the wrapper to let the O2 in slower - less heat but over a longer period. When you get home, remember that it'll take time, not insigificant, not just to get your bags, leave the airport, and get home, but also to unpack each plant and repot it. Hopefully you'll be more prepared for the repotting than I was when I arrived. :Þ. Oh, and of course, hope your bags don't get lost or damaged! And then, settle in for the time it takes for your plants to reestablish themselves and heal. 4 months later my passionfruit still has some really ugly damaged leaves from the transport. They bug me, but they're still green and contributing to the plant's health, so I don't want to remove them.
And that's just about the transporting of the plants, let alone getting them approved for export/import!
Yeah, it's a pain to transport live plants with you internationally.