I think you'll break even in about 6 trips if you factor in park hopper and parking for Believe. I live about 12 minutes so not so helpful in commenting on the commute. I'm the AP that Disney wanted to cut down on.. I go spontaneously and usually just for a few hours. I think for my last full year AP I was past 30 trips. It really comes down to how you and your family like to do disney. I realized I am not a rope drop and stay til closing type of person. I just went the last 2 days and since I was paying for the ticket, I tried to stay as long as possible to maximize what I paid for. I even stayed at Grand Cal DVC for a night to avoid paying for parking.

I can't wait to have an AP again so I can go back to how I enjoy disney. One thing I did notice was my first year as an AP a few years back, I got a pass without parking, and so I ended up going just 6 times that year. Its a psychological game I supposed but I know not having to worry about parking fees help make those few hour trips doable. I think you should definitely get the passes since you seem so excited and this way you can see how your family utilize it. There's still a few unknowns about the passes like how many reservations are available and how fast they book out, etc You can try out the different commute methods and see what might work best for you. I don't think it'll be hard to go at least 6 times to break even at least.