Even if the chest in the homestead is full, you can still right click to send items there... but they don't appear in the chest.
Where do they end up?
I know your inventory and backpacks appear to have unlimited space until you hit the max weight on that character, meaning every time a row is full it starts a new row. Now I'm assuming chests work the same way, except since chests don't have a weight limit then they should by logic, have infinite item space.
Can you scroll down through the chest?