  We investigate the gravitational interaction between low- to
intermediate-mass planets ($M_p \in[0.06-210]\,M_{\oplus}$) and two previously
formed pressure bumps in a gas-dust protoplanetary disc. We explore how the
disc structure changes due to planet-induced perturbations and also how the
appearance of vortices affects planet migration. We use multifluid 2D
hydrodynamical simulations and the dust is treated in the pressureless-fluid
approximation, assuming a single grain size of $5\,\mu{\mathrm{m}}$. The
initial surface density profiles containing two bumps are motivated by recent
observations of the protoplanetary disc HD163296. When planets are allowed to
migrate, either a single planet from the outer pressure maximum or two planets
from each pressure maximum, the initial pressure bumps quickly spread and merge
into a single bump which is radially wide and has a very low amplitude. The
redistribution of the disc material is accompanied by the Rossby Wave
Instability (RWI) and an appearance of mini-vortices that merge in a short
period of time to form a large vortex. The large vortex induces perturbations
with a spiral wave pattern that propagate away from the vortex as density
waves. We found that these vortex-induced spiral waves strongly interact with
the spiral waves generated by the planet and we called this mechanism the
"\textit{Faraway Interaction}". It facilitates much slower and/or stagnant
migration of the planets and it excites their orbital eccentricities in some
cases. Our study provides a new explanation for how rocky planets can come to
have a slow migration in protoplanetary discs where vortex formation occurs.
