Susan and I pull our two dogs in a Burley kid trailer (older, purchased used, not sure of model name) all the time. It is much less noticeable behind the tandem than behind my half bike, especially on uphill. On the half-bike the trailer alternates between pushing and being pulled, where the tandem has enough momentum that it pulls all the time. Another issue is when you need to back (off the bike, natch) the rig...the bike will turn so slow that it is really difficult not to jack-knife the trailer. Lifting the front off the ground and steering with the back wheel fixes this.
You have to keep in mind where the trailer wheels are going, and it is waaaaay back there. I spilled the dogs once by clipping a curb. To avoid this, you need to start right hand ( left for you limeys) turns late. But this usually means a sharper turn, so you need to slow more so the trailer (two wheeled trailer) doesn't spill. Yup, did that once too.
First post here, BTW: Kevin and Susan from Albuquerque. We picked up a Bilenky off ebay a couple months back. Hope to be in good enough shape for centurys next spring.