Context. We present a detailed analysis of the extended structure detected around the young and close-by Herbig Ae/Be star R CrA. This is a young triple system with an intermediate mass central binary whose separation is of the order of a few tens of the radii of the individual components, and an M-star companion at about 30 au. Aims. Our aim is to understand the nature of the extended structure by means of combining integral-field and high-resolution spectroscopy. Methods. We conducted the analysis based on FEROS archival optical spectroscopy data and adaptive optics images and integral-field spectra obtained with SINFONI and SPHERE at the VLT. Results. The observations reveal a complex extended structure that is composed of at least two components: a non-uniform wide cavity whose walls are detected in continuum emission up to 400 au, and a collimated wiggling-jet detected in the emission lines of helium and hydrogen. Moreover, the presence of [Fe II] emission projected close to the cavity walls suggests the presence of a slower moving wind, most likely a disk wind. The multiple components of the optical forbidden lines also indicate the presence of a high-velocity jet co-existing with a slow wind. We constructed a geometrical model of the collimated jet flowing within the cavity using intensity and velocity maps, finding that its wiggling is consistent with the orbital period of the central binary. The cavity and the jet do not share the same position angle, suggesting that the jet is itself experiencing a precession motion possibly due to the wide M-dwarf companion. Conclusions. We propose a scenario that closely agrees with the general expectation of a magneto-centrifugal-launched jet. These results build upon the extensive studies already conducted on R CrA.