Active Family Sims left home while one is on vacation

Yes, they automatically go to school/work. Even if (if you have seasons) it's supposed to be a holiday - that is you've set the day to be a day off from work/school.

Children will not do their homework, but their grades will not decline. (In my experience, grades don't decline from not doing homework even under normal play, but then, I've tended to get them up to A's before I let them ignore it.)

Everyone back home should be fine when you get back, too. :)