I too have a 10 yr old girl who can be challenging in the morning. I know she likes to have warm clothes in the morning so each night her and my 5 yr old boy pick out their clothes and toss them in the dryer and in the morning before I wake them I start the dryer for about 10 mins. I also moved their bedtime to between 8:30 and 9 and have her take a shower in the morning as this seems to help her wake up. You can also try waking her a few minutes earlier than your other children.
It is very important to realize that she is still young and even though as an adult you may be able to wake up with a little bit of sleep, her wake/sleep requirements a very different. Instead focus on the times she gets up with less coaxing and tell her how proud you are that she got up after only, say, 5 min of coaxing, include her thoughts in a plan to help her wake up (that will make her feel more in control and apprecitated) and most importantly, dont compare her to your other children. All children are unique in their habits, especially within families. Comparing her to the other children can leave her feeling that she is not good enough and adds to any existing sibling rivalry.
I too am a mother of 4 children (14, 12, 10 & 5) with a full time job. I find that children can be very clever (especially the older ones) at coming up with ways to get extra attention even if it may be negative.
So have patience and try to see it from her point. This is all temporary, they grow up soo fast and one day you may find yourself longing for these days back as a respite from the teenager who just rolled her eyes at you and acts as if you are the biggest idiot in the world.
Best Wishes J.