How to determine the number of water ligands attached to Pd in palladium chloride aquacomplex PdClₓ · yH₂O?
I hope the following two references would help you find the way. I honestly think Ref.1 shows much more promise, abstract of which states that:

Monomeric palladium(II) chloro aqua complexes of the form $\ce{PdCl_r(H2O)_{4-r}^{2-r}}$ ($r = [0,4]$) were studied both experimentally and theoretically to gain insight on both the stabilities and the nature of palladium-chloride interactions.
The thermodynamic stabilities of these complexes were studied in aqueous solutions from $5$ to $\pu{125 ^{\circ}C}$ with UV-vis spectrophotometry using a quartz flow-through cell. Tentative measurements up to $\pu{200 ^{\circ}C}$  were also carried out in pressurized titanium and gold-lined optical cells but revealed important losses in soluble palladium. The strong ligand-to-metal charge transfer bands of the palladium complexes below $\pu{350 nm}$ were used to constrain the step-wise thermodynamic formation constants at each temperature, using results of singular value decomposition of the spectra over a broad range of palladium:chloride ratios and wavelengths. The temperature-dependent constants were used to obtain changes in enthalpy and in entropy for each reaction. The thermodynamic stabilities of $\ce{PdCl(H2O)3^+}$, $\ce{PdCl2(H2O)2^0}$, and $\ce{PdCl3(H2O)-}$ are larger at higher temperatures, whilst the one of $\ce{PdCl4^2-}$ is smaller. All changes in entropies are positive for the former three species, but negative for the latter, presumably due to a larger solvent reorganization around the doubly charged $\ce{PdCl4^2-}$ species. The room temperature thermodynamic values derived from this study are also in agreement with previously published calorimetric data.
Theoretical calculations on the intramolecular distributions of electrons in the different palladium(II) chloro aqua complexes, using the methods of atoms in molecules and of the electron localisation function, showed $\ce{Pd-Cl}$ and $\ce{Pd-OH2}$ interactions to be of largely closed-shell/ionic nature. These interactions induce an important distortion of the outer core shell electrons of $\ce{Pd}$, as well as stable accumulations of electrons between adjacent $\ce{Pd-Cl}$ and $\ce{Pd-OH2}$ bonds known as ligand opposed core charge concentrations.

References:

J.-F. Boily, T. M. Seward, “Palladium(II) chloride complexation: Spectrophotometric investigation in aqueous solutions from $5$ to $\pu{125 ^{\circ}C}$ and theoretical insight into $\ce{Pd-Cl}$ and $\ce{Pd-OH2}$ interactions,” Geochimica et Cosmochimica Acta 2005, 69(15), 3773-3789 (https://doi.org/10.1016/j.gca.2005.03.015).
L. Espinosa-Alonso, K. P. de Jong, B. M. Weckhuysen, “A UV-Vis micro-spectroscopic study to rationalize the influence of $\ce{Cl-(aq)}$ on the formation of different $\ce{Pd}$ macro-distributions on $\gamma$-$\ce{Al2O3}$ catalyst bodies,” Phys. Chem. Chem. Phys. 2010, 12(15), 97-107 (DOI: 10.1039/b915753k).