"Yesterday my sister-in-law came to my home."

Translation: Hieraŭ mia bofratino venis al mia hejmo.

[BradfordBowman]

I tried to replace the preposition with the accusative like so: "Hieraŭ mia bofratino venis mian hejmon." But this was marked as incorrect. It seems to me it should be correct. I understand that use of the preposition together with the accusative would generate a different meaning (movement into the house), but as I didn't use both, I thought I had a valid translation.

[Lovaniensis]

*al miaN hejmoN is a grammatical impossibility. The accusative is used to signify "motion toward" only with prepositions which by themselves do not signify motion. Like so:

en="in", sur="on". These prepositions by themselves signify location, not motion.

Mi estas en la parko. I am in the park.
Li saltas sur la lito. He jumps on the bed.

vs.

Mi iras en la parkoN. I go into the park.
Li saltas sur la litoN. He jumps onto the bed.

[johmue]

The verbs of motion (iri, veni, ...) are used intransitively. That means, they don't take a direct object. That probably is to avoid ambiguites like "into my house" vs. "to my house".

[Lovaniensis]

Theoretically, just about every preposition can in principle be replaced by an accusative. In practice, this is done only sparingly.

In everyday Esperanto, a sentence like "Ŝi venis mian hejmon" is rare. Some hearers/readers would find it special, others would find it weird.

[BradfordBowman]

OK, thanks, that helps.

[PetziPotato]

Why not "Hieraŭ mia bofratino venis al la mia hejmo"?

[SeanMero]

"Yesterday my sister-in-law came to the my home." Mia hejmo is already not indefinite (in that your house is one specific house), so la would be redundant.