What was the meaning of the country song in the episode "Aus der Tiefe der Zeit"?

The Dominik Graf directed Tatort episode "Aus der Tiefe der Zeit" repeatedly employs a certain country song as in-scene background music at various occasions. More or less anytime when some music plays as part of the scene, it is this song, be it at the party of the Löwenhof constructors, Jansen's apartment, the casino where the Croatians meet, and especially most prominently in the Holzer villa, when Peter Holzer commits suicide and later when Liz is arguing with Ante, ...

I am unable to find out what the name of this song was, so first of all, what song was that? But even more important, was there any meaning to this song in relation to the story and its motives, and what would that be? The only slight connection I could draw was, that this very Western-style song might just be an allusion to Magda Holzer's past in the "Annie Oakley Show" decades ago, but that doesn't hold so strong when the song is used at each and every possible occasion and Magda's past as "Annie Oakley" wasn't much significant at all.