How to use proper constraint

I am trying to make a system in which you can grab models and move them around. When I grab a part of a model, that part moves just fine, but the rest of the model doesn’t move with it. Which type of constraint should I use to connect these parts?

If this part is tool, then you need to weld the rest of the model onto the part.

It is a wall made of several pieces(made of different materials so it can’t be unioned), and the welds don’t keep it together while dragging it