Maya Modeling :: Select Entire Group Of Objects To Drag To A Different Position

I'm new to Maya, so this is likely something I'm just missing or that I've done without realizing it, however...

I've created a scene with a few polygonal objects. As an example, imagine a house with plants around it and a cloud above. The plants are spaced evenly along a curve, and the cloud is also made using a Paint Effect with a Modifier around it to control it's shape using slight forces, etc.

However, when it's done and I select the entire group of objects to drag to a different position, weird things happen. The plants seem to move much more quickly in that direction, so that soon they're no longer positioned where they should be at the base of the house, and the clouds move in the opposite direction from where I'm dragging (i.e. down not up). What I'll call the 'normal' polygonal objects (e.g. the house, car, etc.) all move fine, but I cannot figure out how to fix the other items so everything maintains its relative position, or lock the whole scene together to move as a group.

I've tried to combine them, and even 'parent' everything to the house, but I suspect I've changed something like a control handle position or rotated something that now moves opposite the normal xyz directions.