I have to give a strong vote for Aquarium of the Pacific for your day near the port. Shoreline Village is nice but small. There are several restauants in that area though that are good choices. That area of Long Beach is kept up pretty well primarily due to the activity they get during the Long Beach Grand Prix. If you look around you'll see markings on the asphalt for the start/finish line and corners for this popular street race.
I also know you said you can't do
Disneyland but seriously consider Knott's Berry Farm as an alternative. The tickets are much less expensive (
http://www.knottsberryfarm.com/public/admission/prices/index.cfm) and they are really cleaning up the park. They have done a lot of work over the last few months on making things cleaner. You could spend your extra day at Knott's and then do the Aquarium and the LB area on Sunday, since you are flying out on Monday.
You may also consider finding a Hotel near the Ontario airport for Sunday night and spend Sunday at Ontario Mills (as was suggested). It may help your travel mood on Monday morning if you don't have to get up as early to make that trek to the airport. Traffic will also be much better on Sunday mid-day than Monday morning. I know there was that Previous Poster who trashed that option and while I'll agree that the Ontario Mills Mall is a little worn, it is still a very large mall and is a good choice for killing some time.
Here is another thought for you. Even though you can't do Disneyland, you could choose to spend some time in Downtown Disney. They have a much nicer Rainforest Cafe there plus a very nice movie theater. They also have that giant
Disney Store they call World of Disney and plenty of other options as well. You can also kill plenty of time at Build a Bear workshop and/or Ridemakerz. To me, that is a very viable option for your Sunday time.
I am making the above suggestions assuming you don't have a rental car. Each of those can be done by picking up a shuttle from the port area. It won't be free, but not too bad.
If you have a rental car then you could choose to venture out a bit.
One final suggestion for spending your "day". Getting to Hollywood isn't that difficult if you are in Long Beach. You can take the Blue Line from Long Beach to Union Station then take the Red Line from there into Hollywood. See the stars on Hollywood Blvd. Stand on the corner of Hollywood and Sunset, visit the Chinese Theater and even consider taking in a movie at the El Capitan theater if your timing works. Beauty and the Beast 3D opens there today. Just plan for your return to be before dark. If you don't like Hollywood, you could get off at Union Station and you are a short walk from Olvera Street (
http://www.olvera-street.com/html/olvera_street.html) or take the Gold Line from Union Station to Chinatown (
http://www.chinatownla.com/index.php).
There really is quite a bit to do. Depending on how much time you actually have, the ages of your kids and how adventerous you want to be, there are many options.
