There are two US presidents that had their sons elected president. John Adams and John Quincy Adams, plus the more recent George H W Bush and George W Bush. Benjamin Harrison was the grandson of William Henry Harrison.
Teddy Roosevelt has the same last name as Franklin Delano Roosevelt, but they were only fifth cousins. Eleanor Roosevelt was much more closely related to Teddy Roosevelt, she was his niece. Being a fifth cousin is not really that closely related. Teddy Roosevelt was more closely related to Martin van Buren, being his third cousin, twice removed. Franklin Delano was more closely related to Zachary Taylor, being his fourth cousin, thrice removed.
Source: "Theodore Rex" by Edmund Morris provides the interesting genealogical tidbits about the relationship between Teddy Roosevelt and FDR.