"Sie verlor ihren Vater im Alter von drei Jahren."
Übersetzung:She lost their father at age three.
Technically, you can be wrong. Their can be used as in general, usually when you do not know a gender, or want to conceal it. E.g.: One would know their strength. But yes, in this case, it is not correct and sounds unnatural. Same goes for 'at age three'. That should be 'at the age of three'.