If you are capable of riding with the two of them on a cargo bike, then you are capable or riding with the two of them using an Adams tandem trailer. Balance is a problem with these for those who are not used to the weight, but clearly you can handle that. And having the kids work instead of just sitting there should make it easier to keep them under control (I'm also not opposed to blackmail: "If you don't sit still, I'm going to show all of your friends this picture of you when you were 2.")

For whatever reason I just can not comprehend, the trailer comes with a knobby tire. Swapping it out with a slick one will make it easier to balance.