Sims have inventories - large "pockets" that they carry everything up to and including their cars and hot tubs.

One thing that may help reduce lag is not having too much in the Sims' inventories.

To move items from one inventory slot to somewhere else, when there are many, eg many tomatoes, hold down Shift when selecting the corner triangle.

When moving a family, if you have a lot of ingredients etc to take with, or seeds, it's worth investing in a WA chest to store them in. This can then go complete with contents into the Family Inventory and be retrieved once moved.

The Family Inventory is separate from the Sim's Inventory, but some things overlap.