I wouldn't willingly ride 12 miles/day on a cargo bike, unless I had unlimited time and energy (and with four kids, I can't imagine you do) or no hills and a steady cruise with few stops. I have an Xtracycle, it is a pleasant and comfortable ride, but distinctly slower than my commute road bike. I see people riding cargo bikes all the time, if I'm riding 17 mph they are maybe doing 14 mph, and on hills they are turtles.
I'd get a used road bike for $200, spend $100 bringing it up to snuff, and ride that on the commute. Vastly faster than a cargo bike, if it gets stolen or crashed you're only out a couple hundred bucks. Or use your mountain bike with slicks, it is still vastly faster than a cargo bike and it is free.
On the cargo bike, you'd have to think hard about what works. You're at work, wife needs to take the kids somewhere, there is no way she can or will load four kids and two child seats onto any cargo bike and pedal more than a mile or two on flat, slow roads. Its just not realistic, unless she is a total bike nut. I suspect your cargo bike will actually be a "grocery bike".
In your shoes, I'd do the used road bike/commuter and stick an Xtracycle extension on your mountain bike (if it fits) for the grocery duties. Total cost maybe $700 and you;ll have two bikes well suited to their intended uses, as well as some redundancy (bikes do break down).
If you are absolutely determined to use a bike to haul the kids around, at least consider an electric assist for the cargo trike you get.