With these old census records there is no assurance of relationship of people in the household. I have records of people getting remarried and not having children of previous marriage living in the household. There are also cases where niece or nephew would be in the household to help with work but you would not know it if just going by the census records. The Joshua in 1860 had a Louisa age 19 and a younger child. Louise could be a daughter in law or other relation and the younger child could be hers.