We present the results of a combined neutron scattering and magnetization study of the pseudo-one-dimensional magnetic compounds [ (CH$_{\rm{3}}$)$_{\rm{3}}$NH] Co$_{\rm{1}-x}$Ni$_x$Cl$_{\rm{3}}$ .2 H$_{\rm{2}}$O, abbreviated as CoNiTAC. For Co rich samples, we determined the 3d magnetic structure to be canted antiferromagnetic having the magnetic space group Pnm'a'. We performed Monte-Carlo simulations and could reproduce well the measured temperature dependence of the sublattice magnetization assuming an Ising type, spatially strongly anisotropic interaction. The exchange integral along the chains ($b$-direction) is at least 100 times larger than the average exchange in the $a$-$c$-plane. Despite this strong one dimensional character of the exchange interactions the critical exponent $β$ was found to be very close to the theoretical value for a 3d Ising system (0.31). We did not discover any anomaly of the long range order component for the mixed crystals, for which a spin glass phase had been proposed by other authors on the basis of a decay of the TRM on macroscopic time scales. Instead, our polarized neutron diffraction and magnetization measurements reveal that the low temperature dynamics is connected to domain relaxation processes and not to a spin glass transition.