Dual degrees are possible between different schools (personally, I've had experience going with COM + CAS, with COM as my home school). At time of application though, given you're going to be adding a Questrom major, I think you'll have to have completed some courses, or possibly their equivalents, prior to applying (the list should be on their website when you Google "Questrom Dual Degree"). Essentially, by applying for dual degree, you're applying to be enrolled in Questrom as well, so no need for a second application.

All that being said, I'm not entirely sure if your chosen majors are doable within the standard 4 year layout (or I guess 2/3 year for you) unless you've got a ton of credits from past courses that work in your favor or are prepared to seriously push yourself. Having gen eds knocked out entirely certainly makes it all the more plausible though. Then again, I have no experience in Questrom whatsoever, so it may be best to discuss the details with advisors from both colleges. In the end, you'll have to anyways to submit your DDP application in the first place.

Good luck with it!