The answer to this question depends on what counts as a barrier in Hungarian. If Focus Phrase is a barrier and corresponds to IP in English, the extraction pattern will be as follows:
Note that the question word that moves to Spec,FocP is turquoise-colored while the relative pronoun that moves to Spec,CP is blue. As a result of the difference in landing site, the two movements do not interfere with each other. The choice to make the subject DP move to the C-level projection and the object DP to the Foc-level projection was arbitrary. Reversing the landing sites would make no difference in the system we have set up.
For your information, the actual facts of Hungarian are more complex than this exercise suggests.