I have stayed in those interior rooms with three adults and it is just barely manageable. there are two twin beds with bunk beds with ladders for two on top. Close space is limited so take little. The upside of these rooms is it is dark and you never know if it is day or night so you can sleep any time. Down wide is without an alarm you might now wake up.
For your family of 4 take 4 suite cases and limit their size. You can shove them under the bed so those on the bottom can just about use them as a drawer under the bed.
Princess is a great cruise line.