The official order of precedence for female members of the royal family is based on line of succession to the throne, whether your husband's place or held in your own right. So, the closer you are to being Queen, the higher your precedence. It has nothing to do with your title or birth status.
So, Harry's wife would follow William's wife who would follow Camilla. Although their rank is derived from their marriages, Harry and William's wives would come before the princesses of the blood royal who are within the line of succession in their own right.
In general, the royal order of precedence is generally quite different and usually the princesses of the blood royal take precedence ahead of princesses by marriage, although usually the wife of the heir to the throne take precedence ahead of all other females other than The Queen or a Dowager Queen.