Answers to Questions by Yair Davidiy
Why is J. Kushner considered an Orthodox Jew (by news outlets), when he does not wear a hat (even a fedora) and travels on the Sabbath?
https://www.quora.com/Why-is-J-Kushner-considered-an-Orthodox-Jew-by-news-outlets-when-he-does-not-wear-a-hat-even-a-fedora-and-travels-on-the-Sabbath/answer/Yair-Davidiy
The head-covering is not really mandatory though we now usually take it to be.
Concerning Shabat:
Presumably he is driven by others (again we assume by a non-Jew) and does not drive himself. If his presence is required for a decision or advice on a matter that has the slightest chance of involving the saving of life then there is no problem.
All reports of Jared and Ivanka traveling on Shabat were concerned with matters of state and not of pleasure. The presence of Ivanka, alongside Jared, due to the circumstances might also have been of importance.
So too, a doctor can allow himself to be driven to hospital or to drive himself when there is no other option. In fact if he does not do so he would be considered a transgressor.