Caesars dictatorship ends with his dead. In the same moment Antonius is not longer Magister Equitum. And the consuls take over. So IRL, when Caesar died 44 BC, Antonius was consul and therefore in a much better position, than a (ex-) magister equitum. If no consuls are elected, which happened sometimes during a dictatorship, the senate has to appoint an interrex, in order to manage immediate elections. No problem, because the real executive of the roman republic were not the consuls or other magistrates but the senate!
Just a hint for all people, who think that Cicero had a good idea about a reform of the republic: just read de legibus and de res publica and some of his letters dealing with this subject. Ciceros proposals are more than naive. He almost completely missed the basic issues of the roman society and constitution, which led to this mess called late republic. Well, he had some useful ideas about further buerocratization and a so called mediator. Octavian had read Ciceros scrolls obviously. But implemented it his way.
It all comes down to the old question: Was the republic doomed to death (Montsquieu), or did it just need more time to reform itself (Green).
And I agree with Sly: Antonius might be rough, but not plain stupid or suicidal. He simply goes home as a man of private means and starts to play the big game again by looking for new partners.
PS: Was Antonius still Magister Equitum, when Caesar fought in Alexandria?