I can't really tell from the picture -- do you have those tri-couplers bolted together with struts? If not, remember that two parts will generally only connect at one point, so those couplers are probably only linked at one corner. That may be the source of your problem, because it will tend to flop around violently under any kind of acceleration. If you zoom in close and carefully increase the throttle, you'll probably see that the two tri-couplers are flexing through one another in flight.
The probe cores are another possible source of oscillation. It's a bit better, since they're centered, but they're also quite small compared to the rest of the stack, so they could also be a culprit. A set of struts bridging the gap might help that, too.
For the record, multi-docking is terribly tricky. If you don't have the alignment perfect, and I mean pixel-perfect, it won't link more than one of the ports. Even if it does, the docking ports get bugged half the time, so be sure you never want to undock again. You're almost always better off just using a Clamp-o-Tron Sr., or even just a regular C-o-T and a gentle hand on the throttle. Of course, there's also Kerbal Joint Reinforcement, which makes your rockets look and feel a lot more like professionally engineered spacecraft.