I need advice on traveling to Hawaii with the whole family.?

Hawaii tried an interisland Superferry for a few years, but it ceased operation in 2009 and is not coming back. Now, there are only a couple limited ferries like between Maui and Lanai. They primarily help people on the smaller islands get to Maui so they can shop, work, get medical care, etc. Tourists don't commonly visit the smaller islands.

The islands actually are a good way apart. For example, it's 209 miles from Honolulu to Hilo on the Big Island. It's about 90 miles from Honolulu to Maui. It's 63 miles from Oahu to Kauai. You're not finding small boats nor inexpensive cruises covering those distances.

Sooooo... nope. Your only realistic options are indeed just interisland flights or expensive cruises. Most people do the flights.

it's a half day cruise

No, there are no other options. There are no ferries between the major islands. The only ferry that exists is the one from Maui that will take you to Molokai or to Lanai. Molokai and Lanai are small islands and there is not a ton of stuff to do. They're perfect for honeymoons, but not for families looking to sightsee and have adventures. If you want to travel between the other islands, you have to fly.

I don't know how long you're planning on being here, but I never recommend more than one island if you're staying less than 8 days. It's too much to pack, turn in your rental car, go through security at the airport, wait for your flight...and then do it all in reverse on the other island. Pick one island and stick with it. You and your mom will be much happier that way.