i am sorry i haven't read all of the posts, but have a few ideas, i do agree that children need to know there are consequences to their actions, and also you should only ever say things you mean or will do agree( don't make empty threats)
so onto my ideas, sounds like your ds is doing what is needed in getting ready and on time, can you try to reward this behaviour, treats for this e.g a week of on time can equal a treat at the weekend, trip to the park etc? same rules for your ddi, hopefully incentivising good behaviour?
might also be worth considering a little something to do by front door for your ds once he is ready, pack of cards, sorting mini lego figures etc so he isn't just waiting for his dsis, and getting angry.
lastly i would at a quiet time sitting down with them both no tv etc write a morning routine with times, then you become official timekeeper, so you will be saying very positively its 7.30, down for breakfast i. two minutes, or is everyone dressed we need to be readym in 5 inutes, then do a count down with every minute until 1, then every 10 seconds until last 10, then a 10 to 1 count down. this sounds a bit intensive but actually won't take very long, and hopefully will speed up your morning? hope these ideas might help?d