According to reference Elizabeth Pierce b.May 16, 1665, made a will Feb. 12, 1736-7 & was the wife of Isaac Mixer. She was the dau. of Daniel son of Anthony Pierce, her mother was Elizabeth ?, The husband Samuel Smith & Smith children may belong to another Elizabeth with a birth of 1660 & Death date of 1692 and they have gotten confused or the dates are wrong and she was married to both men?
The connected Daniel is the correct father for Elizabeth (m. Isaac Mixer) b.May 16, 1665, made a will Feb. 12, 1736-7, not sure about the mother Elizabeth Shedd, her siblings are listed in the references, John, Ephraim, Mary, Hannah, Joseph, the others Josiah has a different birth (probably confused with his brother Joseph's), Abigail is just a year off, so they are basicly correct.
Her husband Isaac Mixer's will was proved 1724-5, so I don't think she would of married Samuel Smith 08 JUN 1692 in Woodbridge or Piscataway, Middlesex, NJ
