Thank you so much for the great suggestions! I am goin to start implementing them this evening and tomorrow morning. I will let you guys know how I fair. Cross your fingers! :)
Give her more time, a lot of children feel rushed in the morning its nice for to chat and have fun before school, its in your hands get up a bit earlier and then you wont have to hassle her to eat etc,I have seen this happen a lot and my home was a battlefield when my kids had to be got to school it is a matter of taking it slower and not racing them out.
You're right - it's the anxiety that is causing the troubles. Two suggestions - have each child choose and lay out his/her clothes for school sometime in the evening. This will reinforce the fact that they will be attending school the next day. I expect your son might be reacting to the sensitivities of some of the items of clothing or it could simply be the uniform reminds him of school. The second suggestion is to get them up earlier in the morning to allow more time for breakfast. When our granddaughter stayed with us (she suffers from severe anxiety), I allowed her to eat in front of the TV because the distraction lessened her anxiety and therefore, she ate more (it still took about 30 minutes for a small breakfast). Sometimes we have to do what works and not what society deems as appropriate. One other thing which helped lessen the anxiety for our granddaughter was to spend a few minutes with her beloved cat prior to going to school.
Do not be concerned about the the fact that your children "will condition" themselves to this behaviour. If your children do, in fact, have anxiety issues, it is an inherited trait so the anxiety will already exist. But, you are correct - you do need to try to change their behaviour to the stress and this can only be done by lessening their anxiety. Punishments and bribery will not work (but I think you have already figured that out) and neither does an upset or agitated parent. It does get better with time - but I'm talking years and not weeks or months. There is no easy solution. I wish you the best ...
I wonder if you could just switch up the routine - maybe do breakfast first, then shower and dress - so they're not together kind of ramping up in the moments before getting in the car? It seems like a less natural flow of things, to eat then shower and dress, but that would get her to school in the "happy time" after her shower.