We present results from a series of high-resolution N-body simulations that focus on the formation and evolution of eight dark matter haloes, each of the order of a million particles within the virial radius. We follow the time evolution of hundreds of satellite galaxies with unprecedented time resolution, relating their physical properties to the differing halo environmental conditions. The self-consistent cosmological framework in which our analysis was undertaken allows us to explore satellite disruption within live host potentials, a natural complement to earlier work conducted within static potentials. Our host haloes were chosen to sample a variety of formation histories, ages and triaxialities; despite their obvious differences, we find striking similarities within the associated substructure populations. Namely, all satellite orbits follow nearly the same eccentricity distribution with a correlation between eccentricity and pericentre. We also find that the destruction rate of the substructure population is nearly independent of the mass, age and triaxiality of the host halo. There are, however, subtle differences in the velocity anisotropy of the satellite distribution. We find that the local velocity bias at all radii is greater than unity for all haloes and this increases as we move closer to the halo centre, where it varies from 1.1 to 1.4. For the global velocity bias, we find a small but slightly positive bias, although when we restrict the global velocity bias calculation to satellites that have had at least one orbit, the bias is essentially removed.