Ooof! I've so been there...It does get better. My daughter still doesn't like transitions but she copes much better. 5 was probably the worst, but by 8 she's an angel (mostly!) Some things that worked for me...
* shove protein into child's mouth as soooooon as you get them into the car after pick-up; don't even allow them to talk until they've eaten something;
* dump time-outs and consider alternative discipline methods like 1-2-3 magic. This worked OK for us, but you've got to tap into the child's currency.
* break the cycle by interrupting the routine. Catching the bus for a week broke the habit of getting into the car after pick up and storming all the way home.
* increase physical exercise after school so that the child has a way of healthy processing all of their pent up frustration. School can be a very frustrating place to be! My daughter needs at least 2 hrs of exercise a day after school, sometimes more... Gymnastics/diving/acro/bike riding ... are all great for this.
And give yourself a break! This too shall pass...
