I believe Dole is only open until 5pm, and the later in the day you go, the more crowded it is and the lines for the attractions can get long. Parking can also be a challenge. We got to Dole when they opened at 9:30. All we did was the train, browse the gift shop, and get a Dole Whip and it took us nearly 3 hours, and this was in September when its a slower time of year. I agree with PP that if Dole is a must do, it's better done on a North Shore day since it's on the way to Haleiwa.
Just doing some rough estimating - if you go to mass at 7am, back at the Hampton by 8:15am, have breakfast and on the road to Pearl Harbor by 8:45am, that would put you at Pearl Harbor around 9:15am, since its a Sunday and traffic shouldn't be too bad. That would give you about 90 minutes to see the free museum exhibits before an 11am tour. We took about 90 minutes, as people who are not history buffs, and it was about right for us. The tour has a 20-30 minute video and then the ride out to the Arizona. You'll probably be back on land by 12:15-12:30ish. This should put you at Dole around 1:15ish. You'll probably want to grab lunch at some point too, I'm guessing.
Doing the opposite, if you got to Dole around 9:30am, and leave around 12pm (which is about the time we left there when we arrived at opening), it would put you at Pearl Harbor around 12:30ish. This would give you about an hour to explore the free exhibits before a 2pm tour, and virtually no time to grab lunch. You'd likely have time to explore the free exhibits after your tour as well. I think doing it this way would allow you to get to Aulani earlier because Dole won't take as long since it will be less crowded, but you'll be clock watching and pressed for time to make sure you get to Pearl Harbor on time. You'd likely only be able to do one attraction at Dole due to the timing.
I agree with PP that you should choose which one you care more about, and plan around that one. And PP's point about unexpected traffic, even on a Sunday, is valid as well. I believe the Swap Meet at the stadium is on Sundays as well, so not sure how that would impact traffic and parking at Pearl Harbor.