Hello! This is only my 2nd post here as well, but I have a few thoughts that may (or may not) be of help.
In my opinion, undergraduate degrees in music are more about getting experience than about getting a piece of paper: the degree itself won't necessarily qualify you for anything besides graduate school, but the experiences you have might. If you're interested in film scoring, I think some of the most valuable experiences to make sure you are able to have in college are: composing in/getting comfortable with as many styles as you can, learning as much about music production (not always the same as audio production) technology as you can, and collaborating on as many film (or other media or theatrical productions) as you can. Here are a few of my rambling (but hopefully coherent) thoughts on how you might go about this.
First of all, double majoring in composition and business sounds like a great plan given your goals. I don't think it's necessary to study audio engineering: it is likely that a lot of the material would be irrelevant to your musical goals, and you wouldn't learn how to use the technology in a musical way. Instead, I would advise finding a composition department with a very strong music technology program and take all the music tech courses you can. It also helps if the composition profs are into electronic/electroacoustic music: this way, they can help you with the technology and teach you how to use it in musically convincing ways (since writing purely electronic music, which many directors seem to want these days, is very different from writing acoustic music.) I personally would go with general composition rather than jazz composition--the latter might sort of box you in stylistically (since most jazz composition programs, in my experience, are pretty narrowly focused on just one style). In film scoring, it's important to be fluent in a wide variety of styles--including jazz and commercial styles, of course, but many general composition professors will still be willing to help you explore these... at least in North American composition departments!
Second (since, as I imagine you've heard and will keep hearing, knowing the "right" people is extremely important in the film industry), it's a good idea to go to a university with a large/reputable film/media production program, and try to work with as many film students as you can. In my experience, film students are often very excited to get original music for their film projects--sometimes they will email composition professors looking for students to score their work; other times, there may not yet be a bridge between the film and composition departments, so you may have to build it yourself (by emailing film production professors, for instance). Even if you have to work on some pretty terrible films, this kind of thing is really valuable: it gives you experience scoring to picture, a better understanding of the dynamic of working with directors and production teams (which is often interesting, because a lot of the time they don't know anything about music), and, if you're lucky, some personal acquaintances who will keep you in mind as a composer if they keep working on films after graduation.
Lastly (and this is kind of speculation on my part, so please feel free to take it or leave it), I think the second degree in business is a wise choice--and not just because it will put your parents at ease :) For one thing, careers in film scoring don't generally happen overnight, so it's always good to be qualified for a "day job" you don't completely hate in order to pay the bills while you work on independent films, build your portfolio, etc. I think some business sense and marketing skills might also serve you very well in the film scoring industry, where building a reputation for your music as a "product" is so important (hopefully that doesn't sound too cynical. It's just that film studios seldom release job postings for composers--instead, they tend to hire someone whose work they are already familiar with, so knowing how to promote/market your work can be very valuable in making directors aware of you.) Again, this last point is just speculation, and it would be interesting to hear what someone else--who knows more about the industry than I do--thinks about this.
I know it might seem difficult to find a university with good business and composition programs, a strong emphasis on music technology, AND opportunities to collaborate with film students, but they are more common than you might think. For instance, even my undergrad college (Ithaca College in upstate NY) has very good programs in music and film and as well as a passable business school, and that is a fairly small institution... larger universities are likely to offer you even more and better options. Universities in cities with big film production scenes (or lots of film schools) may also be a wise choice. Many small film/visual arts academies don't have their own music programs, so students at such places are often willing to collaborate with composers from other local institutions (that's definitely the case here in Vancouver, for example... UBC composition professors sometimes get emails from film students at other schools in the area who are looking for student composers to write scores for them.) I think those are all of my (long-winded) thoughts for the moment. All of these thoughts are based on my own (somewhat limited) experiences with film scoring, but I hope they are somewhat helpful. Good luck with your decision!