Aims . This work aims to better understand the role of wide brown dwarf companions in planetary systems. Methods . We obtained high-resolution spectra of six bright stars with co-moving wide substellar companions with the high-resolution SONG, CARMENES, and STELLA spectrographs. We used these spectra to derive radial velocities together with a complete set of physical stellar parameters. We then investigated radial velocity signals and discuss the fraction of planets in such systems. We also re-analysed the ages of our targets, which were used to derive the physical parameters of wide brown dwarf companions. Finally, a compilation of systems with known planets from the literature was considered along with our sample to search for possible peculiarities in their parameter distributions. Results . Based on the derived ages of six observed systems, we re-computed the masses of the wide companions, confirming their substellar nature. We confirm planets in the HD 3651 and HIP 70849 systems and find a new planetary candidate in the HD 46588 system. In our survey, which is mostly sensitive to Neptune-mass planets at short periods of a few days and Saturn-mass planets at longer periods of hundreds of days, we derived a fraction of planets orbiting stars with wide brown dwarf companions below 70%, with the uncertainties included. Comparing the parameter distributions of our sample with those of single stars, we observe the enhancement of planets with short periods below six days in systems with a wide stellar companion. Finally, planets in systems with wide brown dwarf companions follow their own eccentricity distribution with a maximum at ~0.65 and have periods longer than 40 days, masses higher than 0.1 M J , and eccentricities greater than 0.4.