This isn't about Obama (or what every other potus has done that's legal), nor is it about any child of a president (including DT's).  I found it odd that your focus was on Obama, which I consider a deflection.  It's this:

Republican Dept. of Education Secretaries:  9
Democrat Dept. of Education Secretaries: 4

The above shows that Republicans have had more chances to change a 'broken' system than Democrats.  Some people don't like the system, but it is better than what DeVos and her followers want -- ala Abraham Kuyper's pillarisation.  DeVos would like it to go beyond the religious aspect, holding to the 'like with like' aspect.

https://en.wikipedia.org/wiki/List_of_children_of_the_Presidents_of_the_United_States