Hi Kristen,
What you're asking for is theoretically possible. There are King rooms at the Pop century which connect to double rooms. In order to accomplish this, you'll need to make a room request. I must caution you that room requests are not guaranteed, but if you take appropriate steps, the odds of you getting your request are quite good.
As a first step, read this post by my friend Bret about
how to make a request. You may also want to head over to the independent website touringplans.com and look for articles called "The Art of the Disney World Room Request" and "Getting the Most Sleep Surfaces Per Dollar."
If you feel like you can't gamble on the possibility of not getting connecting rooms, you may want to look into one of the family suites at either the All Star Music resort or the brand new Art of Animation resort. The suites have two separate rooms, two bathroom, and multiple sleep surfaces, plus a small kitchenette. This is a great value option for blended or multigenerational families.
We're happy to help talk you through the pros and cons of each choice. Just let us know what you need.