Alaska Airlines complaint: Customer Service

My daughter was sent to fly out with Alaska to Idaho this week. We missed her check in time by 10 min and was rescheduled for the next morning, The next Morning we arrive in PLENTY of time. Stand in line to check in and pay for her checked bag and get a pass for me to walk to the gate. we were in line for 30 min. when we finally get to the counter the lady advises us she cant get on the flight because we missed the check in time. And called me a liar becuse she cleared the line 30 min ago I advised the worker that we have been in this line for 30 min and i even showed her my parking pass to show we were there in plenty of time however they kept calling people up who were in first class and bag drops. It was 6 AM and im sorry but if you know you have a plan leaving at 7AM why not make sure the whole 6 PEOPLE in line do not need to get on that plane… why check in someones bags who are not even leaving that day? Customer service horrible. And then i was provided a number to call with a 4 hr wait time to try and get her on another flight.