I have used a Burley trailer from Craiglist with great success. It should fit both your kids and a couple bags of groceries, easy.
Your four-year-old may also be old enough for a tag-a-long bike. We have a Burley Piccolo because I needed the rack attachment, but there are other brands which attach to the seatpost. It may even be possible to pull the trailer behind it. What we use our Piccolo for is family rides--Mr. FP pulls Little Brother (age 4) in the trailer and I pull Big Brother (age 5) on the Piccolo, so he can pedal.
If you wanted to drop four figures, there are all sorts of awesome cargo bikes, including bucket-style ones (like Madsen cycles) and longtail ones. Or Xtracycle makes something (it used to be the Free Radical, but I think it's different now) that basically adds a third wheel behind your bike and holds a couple kids.