It's true that you bought a package, but a package isn't all that. Basically, you got a room (people without packages also get rooms), you got tickets (same MYW tickets as anybody else at WDW). The package tickets don't have to match your resort stay. You could book a Free Dining package with a minimum of 2-day tickets; or book a package with paid dining with minimum of 1-day tickets.
Here's what I'd like Disney to do so innocent guests like you and many others don't run into trouble. MyDisneyExperience should question you, or give you instructions on what to do when more than one ticket is listed per person. If Disney's ticket program isn't sophisticated enough to allow guests to prioritize their multiple tickets in MDE, then AT LEAST, the park entry gate personnel should be alerted to your multiple ticket situation when you try to enter a park, and they should send you to the nearby Guest Relations to have your tickets prioritized.
In regard to your current situation, I know that Disney will fix this for you. But it's a big, ugly, black hole that a number of people are falling into, and it should be changed in some way so this no longer happens. Other theme park operators would die to have people with multiple tickets stacked up, ready to use on current and future trips!