You're on the right track. Goal setting, practice and communication will get you where you want to go. Focus on keeping your upper bodies and heads from bobbing and decide on what style of bike handling you'll use. If you're a bike thrower then your wife needs to go with the flow and you'll both need to work at staying in sync as you pull on the opposing ends of your handlebars such that the bike moves smoothly as you throw (sway) it from side to side. Better yet, set a goal of keeping the bike from moving back and forth so that you waste as little energy as possible when your riding out of the saddles. Make sure that each time you stand you talk about what your objectives are and then after you've finished your push and taken your seats critique yourselves with regard to what worked or what didn't and what you need continue focusing on.
Another thing to consider is you might also want to stay in a lower gear range as you work to improve your technique. Pushing too big of a gear will usually result in exaggerated upper body and arm movements that will be more likely to cause the tandem to flop from side to side, resulting in unintended steering inputs. Bicycles and motorcycles tend to go left or right when leaned to the right or left. So, if your tandem is being leaned over to the right and left on opposite pedal strokes, it will tend to weave up the road unless the front fork isn't absolutely kept on a straight and narrow path.