This is happening because... they are exhausted, after their day of "work"/listening/being spot on/doing things per instruction all day/being in a classroom ALL day/having to sit still ALL day/not being able to just wander around whenever, and they are CONCENTRATING so much all day long. And not to mention, they have to be quiet, all day long and not talk out of turn etc.
School... is tiring. And especially for young children.
When they come home, a child HAS to deflate. And unwind.
They were not playing all day, but working.
My kids, who are now in 1st grade and 5th grade, are the SAME way too, as you describe your kids after school. And yes, IN the car, it starts. As soon as I pick them up. It is not only your, kids.
It is because, they are wound up and need to unwind. AND ALSO... it means, that the child needs food in them. When my kids go for long periods without food, they get low blood sugar... and then it DOES affect their moods/disposition/demeanor...and they get, fussy. So as soon as we go home, I give them a solid, snack. Food. And they can still eat dinner just fine.
I also, have them do homework AFTER they have deflated and unwound.
Even if it is just tracing letters... if a kid is TIRED and HUNGRY and GRUMPY... they cannot do it. They are young children. Not an adult.
For a young child, having to FOCUS all day, and be perfect in school... is TIRING. They come home, and need to unwind.
I would also, get them to bed, earlier.
What time do your kids go to bed???
Mine go to bed around 8:00, but BY 8:30. Even if my kids are different ages.
If they go to bed later... it portends a bad day, the next day.
I KNOW that. AND therefore, it portends a bad day, the next day after school, too.
Also, once my kids get a good solid snack, their mood changes and they balance out.