It does not make a difference on how the ticket was purchased( cash, miles...etc.). All that matters is who the originating carrier is and their baggage policies at the time of booking. In this case HA is the originating carrier for your return trip. Note that HA should only charge you for the inter-island fees, If they try to charge the Mainland fee then only check your bags to HNL then recheck in HNL on CO where the bags should be free. This is more of a hassle, but could mean extra savings for you and your party.

HA interlines with CO to allow the luggage to be transferred.

Now if you are flying first class with HA then you may have your bag fees waived, but the ability to use miles on multitude of carriers doesn't mean the policies of baggage fee exemptions follows you.