At risk of this being a little stream of consciousness, two thoughts:
1. It sounds like the goal is to have the family join you in Seattle at some point; in the interim they are occupying the house in Georgetown and that's not a situation requiring immediate remedy (in other words, you CAN rent something in Seattle, maybe not ideal, but you can afford two housing expenses at the same time). This is important because if you cannot afford both housing expenses at the time it makes your decision making more clear. Can you clarify when they'd ideally join you in Seattle? If it's 6 months from now (say end of spring semester) does that cause problems?
2. If you have any desire to obtain a HELOC you need to make this your first priority. You CANNOT get a second lien on an investment property and the bank is going to be scrutinizing your occupancy. As long as your family resides there (and your spouse is on title) then it shouldn't be hard to prove, but once you've lost the elements we might look at for confirmation (address for filing your taxes, driver's license address, etc.) a bank a won't touch it. I'm a big fan of having HELOC's for emergencies, anyway. You don't want second lien cash out (your alternative to a HELOC) because there's no reason to pay interest on a debt you might end up not needing (the HELOC is mainly for the flexibility to buy something.