Defining "single parents" using PUMS

I'm trying to find out how many single parents in Texas work between 1 and 30 hours per week.

I've used Usual Hours Worked to find individuals who worked between 1-30 hrs per week. However, I'm having difficult with the "single parents" piece. One method I've tried is to look at non-married-couple families (male or female householders with no spouse present) that have their own children in the household, and then use person weights.

However, mixing person weights with household variables seems clunky to me. Do you have any experience doing this? How have you defined "single parents"?