Sounds like you need to have a meeting sweedishmum, with a huge piece of paper so that everyone can have their solutions to the morning rush put down in ink.
Start your meeting by saying that you're finding the mornings very stressful and how you feel - more than likely all your DCs are stressed and unhappy also.
Then ask them to come up with ideas for how to get the mornings running smoothly. Write all the ideas down from everyone.
Then discuss each idea and come up with a solution everyone agrees on.
Then put the solution into practice and see if it works, tweak and repeat until you have a fast and lovely morning for everyone.
If your Dcs are not up to play team, leave them be in their beds, missing the bus - and don't give them a lift - without their lunches (they should be making them themselves at this age) / sports equipment etc and they'll soon look sharpish and take more responsibility for their own lives.
Good luck and remember your teens will surprise you with the solutions they have - try not to blame them for how unhappy you are at the present situation at your meeting - they probably hate all the shouting / rushing also.
Win win, is always lovely! Good luck