Manfred, not Erwin
First of all, you must not confuse Erwin Rommel, the desert fox, with his son Manfred (born in 1928) who was quite well-known for a mayor back in the 1980s.
If I understand it correctly, Rommel tried to become Ministerpräsident (Governor) of Baden-Württemberg when Filbinger withdrew from office. The party favoured Lothar Späth, though.
So ,this should be the first POD.
In the late 1980s, before the wall fell, Helmut Kohl's position as chancellor was undermined within his own party. Lothar Späth was most prominent among them. Kohl, however, managed to keep his grip on the party.
If Rommel succeeds in leading an inner-party revolt against Kohl - he might end up Bundeskanzler by 1987 or 1988. IMHO, this is the only point where Manfred Rommel stands a chance to become Bundeskanzler.
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What is meant by "vice-chair under Franz-Josef Strauss?"
-he cannot be vice-chairman of Strauss' party as CDU and CSU (which is restricted to Bavaria whereas the CDU keeps out of it) are two parties
-he could possibly not be vice-chancellor of a Bundeskanzler Strauss (who lost the election of 1980), as Strauss would have needed the FDP to form a coalition government. They would have had the post of Vice-Chancellor, which is, in Germany, of virtually no meaning but protocolary. The vice-chancellor will not automatically become chancellor for the rest of the term if the chancellor dies or becomes unable to fulfill his or her duties in any other way. The Bundestag would elect a new Bundeskanzler.