Tag-along specific advice that I can pass on.
Adjust the kids seat to the right height & level which will make them more comfortable. As they get a sore backside they tend to squirm.
Make sure that where its attached to your bike is really secure - check often and tighten as required - I find they can work loose with amazing regularity. Make sure there is no slop in the hitch. I found that after a few months of use I had to re-shim an alloy hitch due to wear and tear.
Secure it as low as the seat post will allow.
Pump up the tyres to maximum recommended pressure - easier to tow.
If the kids feet slip off the pedals they tend to cause a bit of movement - you could try toe clips. It doesn't help when they pedal backwards
I use my mountain bike when towing the kids - it has lower gears and better brakes, all of which help - if you haven't got a bike with a really low gear - you may want to think about it now as you'll need it on the Great Vic. - The gears on the free bike are probably a good ratio to compare with.