I say bike seat. I have a big bag of plastic ties that I use to strap the scooter to my bike basket on the way home, that way dd can ride home and scoot to school. I'm not saying it's easy but it is doable. I also used to charge back and forth with them in a phil and teds, and whilst pregnant over the same terrain, bonus point is that dd came out bang on time and with very little effort!
i really enjoy our walks. I think that it's often when problems come out, who is bugging who at school comes out, and really weird questions about stuff pop out. The long walk in has become one of favourite bits of the day. And you will find that it actually rains a lot less than you think! A good rainsuit is a must though, dd loves hers, it's a pink all in one, she looks like that thing out of spongebob in it.
Queen fromars: don't panic! I did it. DS at school DD at playgroup. I did 3 miles ther, 3 miles back. 3 miles there to pick up from playgroup, 3 miles back. 3 miles to pick up ds from school, 3 miles back. It was doable, and i got to be an excellent speedwalker, but again, get a bike with a bikeseat and get your kids biking, safely, and well, from an early age. Ds was without stabilisers by 3 and very secure in biking, it helps enormously if you can bike the diatance.
I still leave a large window for time every day. I make the kids decide the night before, bike, scoot, or walk, and set the alarm accordingly.