An item about how this works,
"it would somehow be "decoupled" and split into two bills. The Senate would have to vote on both (although it's unclear how the House could force this, the Senate being a separate house in the legislature with its own rules, after all)"

While the Senate and House are "equivalent," they are not the same. Spending bills must originate in the House (Recall Pelosi requiring the Senate to come back and vote again for a bill they had already passed).

If the House sends the bill as a whole, the Senate amends it to remove the ACA defunding and sends it back to the House.

What the House is basically saying is that by voting to send this to the Senate, they are voting that if the Senate would amend it to remove such funding, the House is voting to move the bill forward to the Exec Branch without it coming back to the House as an amended bill to be voted on again (or need a Conference to produce a single bill).