I assume this trip is for you, your spouse, and your children? Maybe not, but I'm going to assume at least two people are old enough to get credit cards.

Each adult should apply for BOTH the Bank of Hawaii and the Bank of America Hawaiian Airlines Visa cards. You shouldn't have any trouble getting approved for both cards. Sometimes they will call and ask if you really want both, so just say you need them to separate reimbursable and personal expenses.

You get 20K miles on each card after your first purchase and another 15K miles on each card after spending $1,000 in four months. So if you two of you can spend $4,000 total in four months, then you'll have a total of 4 x 35,000 miles = 140,000 miles. It takes 35,000 miles to get a roundtrip ticket to Hawaii from the mainland, so each of the four cards will give you enough miles for one ticket.

Save the UA miles for something else. If you need a hotel room while on Maui, I highly recommend the Hyatt Regency, although the Andaz will open in about a year. Both are Hyatt properties. When you apply for the Hawaiian Airlines cards, on the same day you should each apply for a Hyatt Visa card from Chase. Each card comes with two free nights at any Hyatt hotel. But these nights expire in a year, so make sure you time it right so that you can actually use them. Or, look at Costco Travel for a discount package. 5 nights at the Hyatt and a car can cost anywhere from $1,500 to $2,500 or more depending on the season.