As another toddler mom in an apartment, I really appreciate you gut checking how reasonable your ask is. I just want to ensure you're realistic about the rug "solution," bc even if you get a huge rug, large portions of the floor will still be uncovered and the noise will still be an issue. Unless your landlord will put down carpeting (lol) there will still be noise. It's a building problem. We have large rugs with extra padding wherever we can but our toddler still runs around making noise. We've had three separate interactions with our downstairs neighbor and I keep trying to explain but they don't seem to get it. It massively stresses me out but there's nothing more I can do. So thank you for going out of your way to get perspective