I don't know whether anyone will read this reply to an old-ish thread, but I finally bought a Bakfiets Long (two-wheeler with a big box in front) last summer in order to manage a long-ish (3.2-miles round trip, or about 5 miles for after-school club) school run with our 4yo and 2yo. It is pretty heavy, but I instantly found it really great for getting around quickly with kids, shopping etc, and wished I'd gone for it four years ago.
However, I still found the school run itself very hard going; the two safest school-run routes out of several fairly rotten options both involve noticeable hills (not that I'd noticed them particularly on my ordinary pushbike, but it's amazing what ~70kg of bike and kids will do for your awareness of gradient) and by the last return journey of the day I was tired enough to find it hard to steer properly at times, which in my expert opinion is not 100% safe in traffic. After a few months of getting wound up about it, it finally dawned on me that it's possible to fit these things with motors. I got that done at the end of January (at the School Run Centre off Mill Road) and it's brilliant. The motor makes headwinds, uphill stretches and heavy loads vanish as far as my legs can tell (even the bridge over the railway line on the Tins path to Cherry Hinton, so steep it's impassible when icy, is trivial in normal weather), I can accelerate away at traffic lights faster than proper motor vehicles, I generally do a steady 23kph without noticeable effort, and I can ride this thing on cycle paths and wheel it along footpaths and park it pretty much anywhere.
The two drawbacks are that older/taller kids might not fit under the rain cover (a tall 5yo might or mightn't), although unless the weather's properly grotty I often just cover the lower halves of my two with the flat luggage cover; and, more substantially, the bike costs very close to 2K new (I paid about 1.2K second-hand, but the preloved Bakfiets market is decidedly brisk) with the motor retrofit another 1.5K all-in. For us it's a car replacement, tons more practical than a car in Cambridge (does the school run in barely more than half the time) with none of the expense of fuel and insurance and negligible maintenance costs, but 3-3.5K is a lot for an optional extra.