I have been there and remember it well.
back then, my morning routine actually started the night before. I would get as much as possible sorted out once all the children were in bed.
lunchboxes made and in the fridge. if you don;t like doing sandwiches the night before (many people don;t I have been reliably informed), then do the rest of the box and just do the sandwich in the morning.
all breakfast stuff bar the milk was put out on the table the night before.
school uniform in my house is always on the banister, but you could lay it out ready on the bedroom floor to be put on as soon as up.
bags packed and by the door.
shoes ready, and coats, also by the door.
morning
get up yourself about 15mins before waking everyone else up....you then have time to bath/shower and get dressed without fretting about where the children are.
then get the children up and get school uniform on straight away. clean teeth, do hair, then go downstairs. No TV until after breakfast and only then if there is time. If baby needs feeding, then do that first (I actually got baby up and fed before getting the girls up. baby then went back into cot/crib until leaving for school......and she was only changed once home).
sort out breakfast and lunchbox.
leaving for school should then be quite easy, as everything else is ready by the door.
the only snag was that occasionally the was a spill and clothes needed changing, but it was actually quite rare, and the simple fact of them being dressed first far outweighed the possible need to change.
HTH