Understanding the structure and dynamics of active galactic nucleus (AGN) jets remains a fundamental challenge in astrophysics. Relativistic magnetohydrodynamical (RMHD) simulations have become invaluable in probing these jets' behavior and emission mechanisms. Recent studies highlight the potential of instabilities downstream of recollimation shocks, where turbulence and shocks can accelerate particles to high energies, potentially explaining the extreme variability observed in high-energy peaked blazars. However, strong magnetic fields may suppress these instabilities, leaving their exact nature and influence an open question. This work explores the development and impact of instabilities downstream of recollimation shocks in AGN jets. Using high-resolution 2D and 3D simulations, we take an initial step toward advanced RMHD modeling with the PLUTO code. Our findings aim to improve the understanding of AGN jets' non-thermal emission, shedding light on their complex dynamics.