I am going to let you in on a secret.  Someone, a teacher/mentor, once told me. (Unfortunately I have a bad memory and don’t specifically remember who it was).  

Always keep any extra pair of clothes in your carry on.  If you don’t have a carry on then in your purse/small hand bag.

When traveling by plane, it can be pretty unpredictable.  A child could spit up or spill on you.  You could have a delay and get stuck without your luggage.  There is always the danger of getting sick and having an accident. Yes, that does happen. Never to me but I know some who have.

If traveling by ground transportation: car, train or bus.  This still applies.  Normally we have a small bag in the back of the car with  an extra change for all of my girls.  And for us, if it’s a long trip.