I've toured on our tandem using a trailer with front/rear and just front panniers, and I couldn't detect any difference in handling. With such a long wheelbase, weight distribution is not nearly as important as on a single bike.
Presuming that your trailer isn't for your child and just for clothes etc. Try leaving the hair drier, kitchen sink, jeans etc at home.
We've just managed a 6 week tour carrying all our gear for cooking and camping using front and rear Ortleib panniers as well as their Rack Pack and medium handlebar bag.
If you have more space you will fill it.