They would not have attempted any relocation. Just made sure they had access to food and water.

As for the pokemon showing up in New Bark -- they were not mysteriously zapped there without explanation (at least not from the Pokemon's perspective). For humans like mom, it'll seem like the pokemon all appeared there without explanation, but if one were to ask the pokemon, they'll mention that Arceus appeared and told them their trainers would be arriving back in New Bark, before lending a hand a moving them all there.