This is such a sad poem. There are a couple of places the wording doesn't quite flow.

The first line "This cradle that I once put you to sleep" doesn't seem like a complete thought I would word it "The cradle were I once put you to sleep."

I think that "It must've been me and not you, my little baby." should be "It should've been me and not you, my little baby." It seems to flow better.

I would reword "At how beautiful the world's expanse." to "At the world's beautiful expanse."

With this "You laugh at each tickle, every time you spill his cup." did you mean "your cup"?

One final note in a poem like this I would put the author's note in a dropnote so as not to clutter up the poem.