May and September are both nice weather for DL and Hawaii, so no worries there. September may be slightly less crowded.
Try to stay at the
Disneyland Hotel or Grand Californian if you can afford it. If not, I would personally skip Paradise Pier and stay at an off-site hotel that's within walking distance. 2 days at DL should be plenty to hit what your family wants to go on, but if you get an early enough flight you could also hit some rides your arrival night.
Aulani is amazing but I highly suggest you have a car and explore Oahu. Food choices at the resort are pretty limited, and there is a lot more available right down the highway.
Pearl Harbor and the North Shore are must do's. There are also several hikes and lookouts around the island. I really enjoyed the hike to Ka'ena Point, Kawela Bay Beach Park, Makapuu Point, and the Halona Blowhole.
There are some great coral reefs to snorkel at, and you can take beginner surf lessons around the island.
Suggested schedule:
Day 1 - fly to LA, get to DL, enjoy Downtown Disney
Day 2 and 3 - Disneyland w/ park hoppers and Max Pass
Day 4 - Fly to HNL
Days 5 - 9 - Full days in Hawaii. At least 2 days outside the resort, more if you rent a car for the whole stay
Day 10 - Day at Aulani, red-eye back to Chicago
You might be able to add one day to DL and subtract one from Hawaii, but I would really recommend as much time on the island as possible. It's a lot easier to get back to Disneyland.