We have been experiencing a rough idle ( shuttering)when in park drainage on 2 brand new batteries as well as a low oil pressure light. What could this be?

 

Some of the later model vehicles require that the computer be "notified" a new battery has been installed. This requires a capable scan tool.Until this is done the charging system will not work properly.
The low oil lite needs to be confirmed with a actual pressure gauge to confirm pressure is up to spec. What is done next is dependent on what gauge reading are obtained.
Rough idle problems can also be checked out with the scan tool. What kind of maintenance has been done to the vehicle?