There are four different things going on because of the history of Hawaii's trying to get tourists to Hawaii. From the DOT website...
"The pre-travel testing program for COVID-19 will start Oct. 15, 2020. Pre-travel testing enables travelers to avoid a mandatory 14-day quarantine if they are tested no earlier than 72 hours before their flight arrives with an FDA-approved nucleic acid amplification test (NAAT), performed using a nasal swab, and can show proof of negative test results from a CLIA certified laboratory." And from the DoH website...
"[T]he state will accept test results from other sources so long as they meet the testing parameters set forth by the DOH, which are an FDA-authorized NAAT test processed by a CLIA certified lab."
So one, Hawaii is saying that you can use the lab of your choice as basically any mainland lab that does 'real' NAAT testing is CLIA certified. So you can get your 11 year old (or 11 month old) tested at your local provider. The trick is to find one that tests young children and gets results back in 24 hours but they exist (at least in NY). In NY these tests are necessary to get your kid back in school if they are sick.
Two, Hawaii naively reached out to partners that they thought could handle COVID testing in volume and with quick turn around time for mainland tourists - Kaiser in CA and CVS nationwide. A complete bust thus far.
Three, Hawaii (and in particular Kauai) has been trying to work with large scale resorts to create 'travel bubbles'. Not for us, but there is likely a market.
Four, Hawaii has been trying to get the US government and the governments of Japan, Australia, New Zealand, to allow tourists from countries that have more or less contained COVID-19 to visit Hawaii. Still a fantasy thus far.