Okay, first--my experience.
In Sep/October of 5th grade, we moved from PA to SC as my mother transferred duty stations from Willow Grove NAS, PA to Charleston Naval shipyard in SC.
I have no idea if we moved on a weekend or what we did--but typically you get a few days for the move to show up to your new duty station, which she did.
I was promptly enrolled in school as soon as possible and the school was told immediately that we just moved there but would be in New Orleans for 2 weeks b/c my mother had to attend mandatory training for something. (We stayed at the base on the west bank in the Navy Lodge--oh joy.

).
All told, I was out of school for at least 3 weeks between the travel time and time away and maybe even up to 4 weeks. The school provided a packet (interesting that they were able to do this quickly for a student they had no idea would be showing up on their doorstep.)
I transitioned JUST FINE--though my biggest challenge were spelling tests b/c they were spelling/vocab (so you had to know the word she was defining and spell it correctly) and we didn't really do that at my former school.
I passed the grade and was even placed in the gifted program the following year. I have no idea how they handled my absences--but they really couldn't punish me or my mother for something that the Federal govt was requiring her to do, so they didn't.
****Now--an alternative to all this is that you can unenroll your kids before the trip to "homeschool" and then renroll them upon your return.
It is an unorthodox thing to do--but people have done it here in Florida as the law permits that. (Most are trying to legitimately homeschool and either tried public school and it didnt' work out or tried homeschool and it didn't work out--but I have known several who have done very brief attempts.)
You would need to evaluate the homeschool laws for your state and of course be accountable to those laws for the duration of your homeschool.
But that is certainly an alternative to getting around the absence issue.
Perhaps photocopy textbook pages in advance so that your kids can work on the actual school subjects--and it wouldn't cost you much money. Keep that in a portfolio if required and present it if required when you reregister them. (you have to photocopy since they will need to turn in their books of course.)
You can also have them due some essays on what they have seen to cover writing assignments and make sure you do things that are academically related as part of your touring.
I would not miss out on the trip AT ALL--but as a backup to any issues you might have, the above can be a very valid alternative that would make everyone happy. (Well except maybe the kids

who will now have to do a bunch fo work independently, but then they won't have homework and the work will take much less time than an average school day.)