I have worked as an investigator with CPS and I'm a Police Officer. I also was a single mom for 3 years after my divorce from my AH. In the two states I have worked in (Arkansas and Texas) there is no age for leaving a kid home alone. Generally, 10 years old and up is considered fine. If for some reason the court or dad brings it up they will just want to know that there is a safety plan in place in case of an emergency. Do you have neighbors who they could contact if you couldn't be right home? Do they have a cell or home phone they can use to reach you? Are there rules in place as far as answering the door to strangers or leaving the home without permission?
And, by the way, I have an 11 year old (12 at the end of this month) who stays home every day in the summer at this time. I leave him a list of chores and a writing assignment every morning as I leave. He calls about 5 times a day...but is just fine.