I can't give advice on the diabetes issue, but I can tell you how I was able to get our mornings under control. My oldest kids are 9 (almost 10) boy and 8 yr old girl. We sat down together and talked about how it's no fun for anyone to start our days with me yelling at them. They hate it and so do I, so we decided together that we need to work together to have happier, more productive mornings. We had a family meeting about it so we could all agree on what to do instead of me dictating stuff to them. We made a list of all of the things that need to be done in the morning. This lead to also making a list of what needs to be done before bed, because things like making sure your homeowrk is back in your backpack and your shoes are by the front door BEFORE you go to bed makes for a much easier morning. Running around looking for things as you are trying to get out the door is a stress trigger for everyone! We ended up with a list broken into 3 categories of expectations... what they need to do when they come home on school days, what they need to do before bed (including times for some of the things, like teeth are to be brushed at 8:00, which means at 7:55 you can not decide you are hungry and want a snack!), and what needs to be done in the morning. I gave no rewards for doing what they need to do-- they just have logical/natural consequences when things aren't done. At their age, they soon got it that things needed to be done and that's that-- they took control of it on their own by checking with the list on the fridge and they were floored by how much they were able to get done on their own instead of me shouting at them!!
This is our routine...
On school days, I wake the kids up a full hour before we need to be in the car (luckily their school doesn't start too early, so we get up at 7AM, in the car by 8/8:15ish and they aren't "tardy" until something like 8:40... I know some schools start much earlier), and tell them I'm getting in the shower and expect them to be dressed by the time I am out. I walk away for a minute and then come back and rewake them in case they have started to fall back to sleep. When I get out of the shower, I go and check to see if they are dressed. I basically say "Are you dressed??!!" and they POP out of bed if they aren't, but fortunatley we've built that extra time in, just in case they're having a slow morning. Then they have the rest of the morning to eat breakfast, brush teeth and hair, get shoes and socks on, and make sure they have backpacks and anything else they need for school. They are not allowed to sit on the couch unless everything is done. If I catch them sitting, I just run through the list- or sometimes I just ask if everything is done and they go check the list themselves.
After school, they are allowed to have a snack first if they want one, and then RIGHT to homework- period. No TV, no computer, no outside play-- nothing until homework is done. We started that in kindergarten. My feelings on this is that they get it done and out of the way and then they have the rest of the evening to play and be kids. If I allowed play first, then it would be dinner and bath and suddenly bed time would be sneaking up on them and when would the hoemwork get done?? Not as big an issue with kindergarten homework, but I wanted to start great habits right out fo the gate because now my 4th grader has over an hour of homework some nights and I wouldn't want him starting that 15 minutes before bedtime! Plus, my kids like to watch a couple of the 8:00 shows (like Kid Nation and Survivor)and they are allowed to since homework is done. Sometimes my daughter whips through her homework and wants to play outside (I don't let them play outside without me) so I check on my son-- sometimes we wait for him until most of his homework is done and I allow him to save one part (like his dreaded writing) for after he gets some outside time, and then he does the rest while I make dinner.
For bed time, they have to have an evening snack overwith before 8:00 or they don't get one. When they forget, I follow through, they whine about how hungry they are as if they hadn't eaten in days, and I stand my ground. The next night, they are sure to watch that clock and eat earlier!! My son needs asthma medicine and it's on the checklist so there is no fight about it.
Good luck! I know it's aweful trying to get out the door! But I no longer scream or stress.
Oh, one more thing. If your daughter still refuses to do homework... a)she is not allowed to do anything else until it's done, and b)find out what her teacher's consequence is. My son had a cub scout meeting once and forgot he still had part of his homework to do and was too tired to stay up and do it. I told him he could wake up early and do it or take the teacher's consequence. He said the consequence was at recess he had to walk the track instead of play with his friends, plus he had to still do the homework the next night. He decided it wasn;t worth it and woke early to do it the next morning. I actually woke him at regular time, but since we have a whole hour to get ready in the morning, he popped right out of bed that day and got it done.