Pretty sure that 'Our Homeland' is the only party Rightward of Fidesz, given that Jobbik is nowadays to their Left. I'm not sure about the KDNP—it's probably a Fidesz satellite party at this point—although I suppose that in the unlikely situation that they have any autonomy left, they could threaten to withdraw support for Orban/Fidesz if he moved Leftward.

Thus I doubt Fidesz even receives any serious pressure from the Right, since all of the parties allied with Jobbik last election were explicitly liberal and/or social democratic.

When Orban was Prime Minister for a few years in the 1990s or early 2000s he was literally a pro-West libtard, exactly the same as Putin. Both men only 'changed' to what they now are as they aged.

Like practically everywhere, things are still shifting Leftward. If anything, Orban already has a total monopoly on the Right and so doesn't really benefit from throwing further bones in that direction. This is why our Hungarian analogues really needs to get behind 'Our Homeland'—only a threat from further Right can stop Orban from instead focusing on trying to increase his support among those who vote for Jobbik, M and DK (which are trying to position themselves as mainstream liberal parties) or MSZP (established mainstream Left/globalist/social democratic party), as would make the most sense to him in the absence of such a threat.