The founding fathers did not have any qualms about descendants of past Presidents becoming President. Consider that John Adams and his son, John Quincy Adams, served as the second and sixth Presidents of the nation, respectively. John Adams was one of the original signers of the Declaration of Independence, and was the primary writer of the constitution for the State of Massachusetts, which served as a major influence for the Federal Constitution.
A weaker example of familial Presidency can be found with William Henry Harrison and his grandson, Benjamin Harrison (made even weaker by the fact that William Henry Harrison famously died 30 days into his term of office), or the much-lauded presidencies of Theodore Roosevelt and Franklin Delano Roosevelt, who were distant relatives with the same name.
Recall that the original Constitution, for all its good ideas, held some ideas that we would consider regressive by today's standards. Only white, property-owning men could vote and, by extension, only they could hold office. That limited the pool of candidates substantially, and would have made it extremely difficult to select individuals who were not from a family previously holding office.
While there may be some issues to discuss in the present regarding overly powerful political families, for the scope of this question: The Founding Fathers did not strongly consider adding in any clauses barring family members from holding an office that they were elected to.
I apologize that I didn't look particularly hard for any laws regarding family members holding offices in countries besides the United States. I can rattle off a list of my own foreseen difficult questions about them, but that won't really answer the question you've written. Suffice to say that, per today's standards and ever-changing definition of family and how families interact, there could be an extraordinary number of extenuating circumstances under which any given law on the matter might be unfair without thousands of explicit qualifiers designed to measure qualities and relationships that are not easily measured.