HI there, I tow my 3yr old twin girls in a trailer nearly every weekend, with my 4 yr old daughter in a childseat behind me too. All this on a steel mountainbike. With them and the gear and the drink bottles and... whatever else, it adds up to over 120lbs extra on a 30lb bike.
Here's a few things that I have noticed over the past year of towing that you might find helpful.
The first thing you notice is that small rises become big hills so you need to use your gears a lot more, the granny cogs are your friend when hill climbing. Standing in the saddle doesn't work as well, so keep up the cadence and use those gears.
The next thing you notice is that stopping is harder, give it plenty of time and slow down when you get to little old ladies walking their white fluffy things on the MUP. In my case I now have to stop about 350 lbs with 4 little pieces of rubber.
Watch gates and gutters, you are now a lot wider and it's all too easy to put the inside tyre over the gutter or come to a very sudden stop in a gate..
Watch out for glass on the path, you now have four wheels to get through the mess.
Always carry a repair kit with you, it isn't just you and a bike that have to walk home if you can't avoid the glass and get a flat.
Oh.. cornering is different, as the kids get older they can lean into the corner but little ones lean with the corner... this can be bad news if you're going too fast, so slow it down.
Keep all your tyres inflated to the maximum recommended. Less resistance means more power actually going into forward momentum.
If you ride with the plastic cover up and you hit a head wind then you are now towing a parachute. If it's windy then the cover should come down.
Remember too, that you're pedalling and getting hot. They aren't and the weather affects them more. So that nice cool breeze thats cooling you down after 10 miles could be the onset of infant pneumonia. Ok so that may be a bit extreme but be aware, we carry a polar fleece blanket, warm but light.
But most of all, protect them too, helmets are a must. Have fun and talk to them as you go. It's a great way to get them interested in cycling. You'll get lots of comments from passers by too, I get mine to wave as we go past to be friendly.