You can also experiment by placing all your household's plants and creations in the household inventory before you save the family and save the house. Then later place house and family in a new game. I don't know if this will work as I haven't tested this theory.
This does work. I figured it out actually because a bug causes some of my plants to disappear upon loading the game. I *think* it happens when my sims are gardening while I save the game and then quit. At first, I didn't think there was anything I could do about it, but then I noticed that my plants AND all of the items that had been growing on them had shown up in my household inventory. Not only did it place the actually plants in the inventory, but it also "harvested them" for me and put the harvested items into my household inventory as well.
Any time you want to move, you can take the plants with you by placing them in your family inventory in build mode.
If you want to take the fridge contents, you can do that as well. You just have to take the items out of the fridge and set them on the floor before you enter build mode.
I recently moved my family to a new home, and this is how I brought all of the plants with them.
Even better, I like to keep the plants in my inventory regularly so that they don't have to be maintained until I need more fruit/vegetables/etc. Since they rarely die in The Sims 4, it is a pain to keep maintaining them. (Also, the accumulation of all the fruits, etc. in your inventory will make the game crash if you don't delete them.)
Putting them into your inventory is a great way around that!