Cargo bikes do handle differently than other bikes, especially when it is loaded up. Almost always, if you're going to fall, it's going to be while you are mounting/dismounting. I recommend to start riding your new cargo bike in an open, empty location so you can get a good feel for how the bike moves without also having to deal with outside distractions. Practice turns, swerving, circles, hopping on/off, etc. You can try getting on and off the bike next to a curb so your foot falls flat and stable on the surface or lower your seat in the beginning until you are more comfortable (not recommended for long rides but it's a good starting point). Also, try to make sure your bike's load is evenly balanced and if possible, keep the weight close to the front of the rack. If one side is heavier, it is easier to lose control. Once you get more comfortable and confident while riding your cargo bike, you will be less likely to tip. Walking with the Mundo is a bit difficult, too. Keep one hand on the brake to help stabilize and move slowly. I also use my hip to help hold up the bike and keep both hands on the handlebars.
That said--tipping happens. Sometimes, it's nice to get that first fall out of the way so you can see that it actually does less damage than one would believe (but I don't advocate doing it on purpose, of course). I have found that I am able to ride with a higher seat now, take tighter turns, and go faster because I am more used to the way my Mundo handles. One last piece of advice: regularly remind your little one to not make too many sudden moves :)