I agree with Mark, do have her anxiety assessed, and definitely with Rosy -- stick with it. To plan to sit in a chair by her bed night after night takes a definite commitment by you. A lot of moms just give in because it will be too time-consuming to take the steps to help their kid break the habit, it's easier just to conk out in your bed at bedtime even if she is there than it is to sit up with your kid in her room. But if you want her to break the habit, you have to help her, not just bribe her or punish her. She will feel better if she knows she can sleep in her own room, will feel more emotionally strong. When a kid is having trouble getting over a hurdle like this, there is nothing wrong with helping her get over it, rather than just making it her problem and either trying to bribe her or to force her. I think at age 10, with her full awareness that this is a habit she should break, she will try. That is a big plus. Good luck!!!
If your daughter experiences excessive anxiety, there could be an underlying emotional issue at stake which very well could be preventing her from sleeping on her own. If you tried everything as you state, you might need to have her evaluated by her pediatrician to find out why she is experiencing so much anxiety as well as seeking treatment for this anxiety.
I agree completely with Annie and most importantly STICK with it! Alot of times kids do things bc they know they can! Ie: mommy is going to feel sorry for me and give in. I have 4 children so im not just saying this. I know from experience! It may take a couple of weeks but you can do it... Start by reading in her room until she falls asleep and then a few days later taper your time in there. No matter what tho if she comes into your room TAKE HER BACK TO HER OWN ROOM! Do not give in at all or all your work would have been for naught and the cycle will continue...
You might try getting an itty bitty book light and sitting by her bed in a chair as she falls asleep every night, reading your book to yourself (in other words, reading an adult book) and letting her touch you if she wants. It might take an hour at first, but sooner or later she could be able to go to sleep that way.