Einstein had no PhD students, although he did famously collaborate with junior colleagues on the EPR paradox. He had three children:
Her fate is unclear. She may well have died young, although this has not been confirmed.
He became a successful engineer. For instance, there is a prize named after him.
He started studying medicine but developed Schizophrenia.
As has been pointed out, there is no clear relationship between a parent's/PhD supervisor's ability and that of their children/students. However, there are some famous examples. For instance, the following fathers and sons won the Nobel Prize in Physics:
- William Bragg and Lawrence Bragg in 1915 for joint work
- J.J. Thomson in 1906 and George Paget Thomson in 1937
- Niels Bohr in 1922 Aage Niels Bohr in 1975
- Manne Siegbahn in 1924 and Kai Siegbahn in 1981
One specific history-related example: The historian Conrad Russell was the son of Bertrand Russell.
There are also some example of whole families of gifted individuals:
The Bernoulli family of mathematicians.
The Curie family: Marie Curie and her husband Pierre Curie won the 1903 Nobel Prize in Physics. Marie Curie was again awarded a Nobel Prize in 1911, that time in Chemistry. Their daughter Irène Joliot-Curie won the Nobel Prize in Chemistry in 1935.
The Darwin–Wedgwood family included Charles Darwin and Francis Galton. (Yes, Galton had some detestable opinions, but his contributions to statistics are fundamental.)
As for famous scholars having famous PhD students, here are a few examples (I'm a mathematician and so my selection is skewed towards mathematics):