If AP controls Feather, the Redeemed and Dreadhorde Arcanist, and casts a spell that targets with Dreadhorde Arcanist's attack trigger, does the spell get returned with Feather's ability?

Assuming the creature AP targeted is one that they control (so that Feather's ability triggers in the first place) and nothing else interferes, then yes, AP can return that card to their hand at the beginning of the next end step.

The effects from both Feather, the Redeemed's ability and Dreadhorde Arcanist's ability each want to replace the action of putting the card into its owner's graveyard with doing something else, so AP chooses one of those effects to apply (even though both effects want the card to end up in exile, they're still separate effects). AP can choose to apply either effect–the other will then no longer apply and will do nothing. Choosing to apply Feather's effect will create the delayed trigger that will return the card to their hand at the beginning of the next end step. (Choosing to apply the Arcanist's effect instead would result in the card not returning, but nobody's going to do that.)