D.B.
Something's off here. It's hard to tell if your husband is dropping the ball, or your parents, or both.
I think your kids need to travel to see their father during longer breaks. If they see him so infrequently, I can understand that there's not a lot of devotion to homework. I also think your husband can keep a supply of clothing for them to minimize the amount of stuff that needs to be packed.
I also question "failing school" at 8 years old. Does he have mediocre grades that are not up to your standards? Are you pushing academics so much (with essential homework, extra tutoring for 2 kids, one of whom is just 5)???? It may be that you have created a complicated system and it's hard for someone else to follow it. I can't believe that a 5 year old needs tutoring for ANYTHING or that a week away will cause terrible homework problems. You need to not send your kids away during a school week during which they have homework, or the school needs to NOT assign projects during a vacation period.
It would seem that the "golden opportunity" is for them to visit their father, not to catch up on work that wasn't done when they were home with you (due to illness). There shouldn't be such difficult academic schedules at ages 5 and 8.
I think you can allow for work to be done ON THE PLANE, and that's it. Still, it all has to come back, so that's a problem. I'm not sure what country they are flying to or how long the flight is, but surely there is "down time" en route and waiting in airports. Again, I'm not sure why they should spend their visit with their father doing anything but bonding with him and experiencing life in the other country.
It may be that others feel you are micro-managing them, from work schedules to packing schedules to initials and stars. You want everyone to follow your system, which you have set up over time, but which is foreign and unfamiliar to them. It's got to be less expensive for your husband to keep some clothes and supplies at his home than to pay baggage fees to ship everything along with the kids. And it's got to put pressure on the kids to know that their time with their dad is supposed to be spent doing things for you and for their school.
I think you could take a photo of all the items packed - lay everything out on the bed or the floor, and take a picture. Then provide it to each child and make a game of repacking every item, with a special prize when they get home with most everything.
You are feeling out of control because....they are not under your control when they are thousands of miles away! So try to let go, expect less. Get them to do more work ahead of time, before the trip - ask the teachers for the advance work. You'll be the "bad guy" at home, but at least it will be under your roof. And you are putting a burden on your children's teachers but asking them to help you replace things! It's not up to them to keep extra copies just in case your kids or their father lose things. It's up to you to either make extra copies, not send the work to begin with, or relax your iron grip a little. You sound like you are carrying a huge load on a daily basis because you are essentially a single parent - but honestly, kids are not going to flunk out of elementary school because they didn't get tutoring at 5 or missed a homework assignment at 8. You would benefit from reorganizing your priorities and by having a conference with the teachers on how best to manage your international household.