It is difficult to hand hold your children and also push the cabin luggage. So as far as possible, I used to avoid carrying any extra cabin baggage except for my oversized handbag which accommodated all the absolute essentials (this is much easier once the children are out of the pampers).
Once on the last leg of the flight returning back from Mumbai to Goa, one daughter fell ill and puked all over me. We had been travelling through the night, because of connecting flights. Coupled with time difference, I suppose the disturbed sleep may have contributed largely to her uneasiness. Having no spare clothing at hand was a huge inconvenience. Luckily the flight was just 50 minutes.
But after that, I always make sure to have at least one complete change of clothes for each of us, on any flight, outbound or returning. This also comes in handy, just in case the check in luggage for any reason goes missing. I keep a copy of all the travel documents in that cabin luggage, in case I leave travel documents on the airport counters by an oversight.
As the children grow, they carry their own change of clothes in their backpack as cabin luggage. We travel very light with just one cabin luggage for each of us that we actually check in. No need to carry too many extra clothes when laundry is possible during travels. And to be even more cautious, I also carry a pouch of essential medication in my handbag (advice to also carry your prescription) and an extra medical kit in the check in luggage. Luckily none of the children have baptised me with their puke again, but I am not taking any chances either.