Q: can I use the positive and negative posts under the hood to maintain power to the computer while replacing main battery

If the two posts are indeed specified for jump starting, then the answer is "yes" you can safely install a 12 volt car battery there at the remote posts while you remove and replace the permanent car battery. Electrically, all you would be doing is adding a 12 volt battery "in parallel" (as opposed to in series which you do NOT want to do) which is harmless because adding a battery in parallel is in fact the technique used to jump start cars. So, what you are proposing fine. All the usual cautions apply in battery replacement though: WEAR EYE PROTECTION; do not short circuit the battery; be sure the new battery is fully charged BEFORE you install it; check date code on new battery BEFORE buying it; measure charging system output after you are done; and never run car without a battery because that WILL destroy the PCM. If you want the battery professionally installed by a certified Mechanic, dispatched by YourMechanic right to your location, please request battery replacement and the responding certified mechanic will take care of this for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.