My little boy is 2 years old plus a few months, and since a while (3 months?) we don't use the trolley anymore. I could be a matter of life habits: we use our bikes when we go in the vicinity, and when we go further, by car, it is usually to places like lakes or mountains where trolleys are useless anyway, and then we bring a "baby-backpack". I also can carry him on my shoulder if needed. So I would say: buying a special "two-kids" trolley is probably a bad idea, as it is not necessary and probably not very convenient to use.
There is a comment I don't agree with: "Nothing ruins an afternoon out like an unhappy child". That is not my way to see this. I try to not let my kid, however unhappy, ruin any afternoons of mine, and anyway having or not a trolley should not be a reason for him or her to be unhappy.
This unhappiness thing is an interesting topic. In fact, I actually train my kid to be unhappy, by sometime randomly taking the thing he holds from his hands. He cries a bit, and then I do something else with him, playing with the sand on the streets, or finding another object for him to hold. I expect him to be less dramatically affected next time he is "unhappy".
I think being able to accept that things are not always going the way one like is of the highest importance and should be taught early, to everyone. (I can tell that this lesson has not been learned well, even by some very well-kwon adults!)