More advice than you bargained for, huh? That won't stop me from dispensing my own

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As to the deluxe versus moderate question, I'd recommend a deluxe if it is in your budget. Being a one and only family trip it will provide you with the best possible experience. The deluxe resorts are nicer, obviously, than the moderates, but their biggest advantage is location, location, location. That might also be especially helpful with teenagers. Any of the MK resorts (Poly, WL would be my recommendations) have monorail or boat access to the MK, and fairly accessible monorail transportation to Epcot. The Epcot resorts (BC or BW would be my recommendations) have walking or boat access to Epcot and MGM. Having that convenience of access to the parks is wonderful. Add to that bigger rooms, better pools, nicer amenities, etc. and you get the best possible experience Disney can deliver.
If you have to go with a moderate I second the recommendations for POR. It has the best theming of any of the moserate resorts and the most "Disney" experience to be had at a moderate. You really feel like you've entered the Old South.
If cost is an issue (and when isn't it) and you want the deluxe treatment then the Wilderness Lodge is a great choice. You get a deluxe experience at a price that isn't as steep as the Poly, BC or BW. The rooms are a bit smaller, but otherwise the resort is up to par with any other deluxe.
As for privacy, that would be nice....although I'm not sure renting a 1Br from a DVC member provides the greatest value that time of year. Then again, Disney's pricing may be high over the Easter period and I have no idea what kind of discounts you might find, so maybe it is a good option. 4 nights (Sat - Tues) at the BCV or VWL would require 195 points. At $10 a point that is $1,950, or $487.50 a night. Compare that to the quotes you've gotten and see how it stacks up. You could also rent a studio from a DVC member, which would require 100 points that time of year and cost $1,000, or $250 a night. No privacy for mom and dad, but it would be hard to beat the price on a great room that time of year. The only consideration you have to take into account with rentig DVC points is that you don't have the same flexibility to cancel or change dates as you would if you booked something through Disney.
Have fun deciding.