I am not here to question anybody's travel arrangements, but I would definitely make time available to spend at least one or two days on this remote magical island instead of doing a direct turnaround and spending around ten hours (feeder flights to SCL not considered) in the air, especially if you have not been to Rapa Nui before.

Also, it is highly unlikely that you will see the "new" Business seats on that route. I have checked a few dates towards the end of May and all flights show the old 2-2-2 configuration.

Technically, booking such in and out in one day is feasible. I spotted prices around USD 800.00 which sounds not too bad. If you leave on LA 841 in the morning, you will roughly have 4.5 hours on the island, before taking LA 844 back to SCL in the later afternoon. Theoretically, this would even allow for a quick tour around the island, but would imply purchasing the national park entrance fee. If you would absolutely like to skip this, your choice would be staying in town which, as far as I know, would be free of charge, yet nothing exciting.

You will have to clear immigration at SCL and walk over to the domestic terminal, where you will find a separate entrance for flights to Rapa Nui. They require an entry form to be filled in and, as a tourist, you are not entitled to stay longer than 30 days (no risk in your case to exceed this, though ).