You're travelling en masse, so I doubt anyone is going to confront you. You may get some scowls if the older kids are unruly, but I think the other passengers will realize they must just grin and bear it if the 2 year old plays up.

There are "mutli-purpose rooms" on some trains that you might want to use in the event of an extreme tantrum. I'm not sure what you'll find in there. Perhaps just a diaper changing space? Perhaps some of the regulars here are better acquainted with the facilities.

One big merit to having a green pass is that the elevators at stations tend to be situated close to where the Green cars stop. So you'll have an easier time with strollers etc.