In CePdAl, the 4f moments of cerium arrange to form a geometrically frustrated kagome lattice. Due to frustration, in addition to Kondo and Ruderman-Kittel-Kasuya-Yosida interactions, this metallic system shows a long-range magnetic order (LRO) with a TN of only 2.7 K. Upon Ni doping at the Pd sites, TN is further suppressed, to reach zero at a critical concentration xc≈0.15. Here, by using muon-spin relaxation and rotation (μSR), we investigate CePd1-xNixAl at a local level for five different Ni concentrations, both above and below xc. Like the parent CePdAl compound, for x=0.05, we observe an incommensurate LRO, which turns into a quasistatic magnetic order for x=0.1 and 0.14. More interestingly, away from xc, for x=0.16 and 0.18, we still observe a non-Fermi-liquid (NFL) regime, evidenced by a power-law divergence of the longitudinal relaxation at low temperatures. In this case, longitudinal field measurements exhibit a time-field scaling, indicative of cooperative spin dynamics that persists for x>xc. Furthermore, like the externally applied pressure, the chemical pressure induced by Ni doping suppresses the region below T∗, characterized by a spin-liquid-like dynamical behavior. Our results suggest that the magnetic properties of CePdAl are similarly affected by the hydrostatic and the chemical pressure. We also confirm that the unusual NFL regime (compared with conventional quantum critical systems) is due to the presence of frustration that persists up to the highest Ni concentrations.