If a mother is fearful of her son's father (who is on parole in another state for first degree murder and arson), how can she gain sole custody in Virginia without exposing herself to his potential harm of her?

To get sole cusody she will have to bring a law suit in family court for sole custody. ( but does she not have custody?? )

Are you wanting to know can you take away the fathers rights, and stop him from visiting the child?

Maybe, or maybe not, you will have to sue in court and try, if if the father is considered a risk, he may still be allowed supervised visits if he want them.

But as for as being at "risk" no, she will have to have the court serve him papers and the such, She can get a order of protection if he is a real threat.

She would have to petition the court (family court) and have a judge decide whether her reasons are valid for requesting sole custody.