It looks like CheckMyTrip is and Amadaeus site; both American and Hawaiian run on SABRE. Thy SABRE's VirtuallyThere.com instead.
I'm not sure if being able to view the reservation on Hawaiian's web site would be much use to you. I have a reservation on HA booked through Panda Travel, and while I can see the reservation online, I can't do anything with it, not even select seats (its a west coast trip; called Panda and they couldn't get me seat assignments either). There's a message at the top of the page showing my itinerary that the reservation can't be modified online because it wasn't booked with Hawaiian.
I don't have a lot of experience with OLCI since I like my real, airport issued boarding passes to keep in a scrapbook, but I suspect you should be able to check in with the HA confirmation number once the 24 hour check in window opens.
As far as the ticket number goes, you'll only have the AA (001) ticket number since they issued the ticket. The only time you'd have multiple ticket numbers is if a travel agency splits a reservation to ticket different segments on different carriers. But they don't always even do that; I once booked a mixed United/Alaska itinerary through Expedia, and all 5 segments (4 UA, 1 AS) were ticketed with a United (016) ticket number. No problems there.