I checked out this article recommended by Jadensmommy. It has very good suggestions and makes sense. You might want to take a look at it. I think it will help.
In the case of your 11 year old, if she is not respecting your rules as a single parent, she is probably not ready to be home alone. You might want to educate her about what it means to be home alone, in terms of safety, emergency numbers, neighbors etc. Then as the above article suggests, I would wean her toward staying home by leaving her for just minutes at a time while you go to the mailbox or next door, or to a store close by.
This is such a very individual matter. One child may be mature enough at 10 and another may be a risk to be alone at 14. The best thing you can do is to understand what the maturation issues are for your daughter and help her to learn what it means to have this kind of responsibility. Then let her have a trial run of 5 or 10 minutes when you think she is ready, and see how she does. You can then train her to be alone in increments of time.
Some parents leave children alone before they are ready, because the parents themselves are overburdened or overstressed. Obviously, this is not the best plan. It is too your credit that you are considering whether the time for this privilege/responsibility is right for your child.
Trust your parental instincts. You will know when the time is right.
The correct age really depends on how the child behaves, but that aside I wouldn't recommend under the age of 14. That is about the time that they want to start proving that they are old enough to do things on their own.