I would offer to clean it up and apologize, but NOT profusely.

Bring a change of clothes for every child/toddler every time you go out. Then you will always be prepared, and won't have to fix a new set until you have to use them.

Until my kids got old enough to manage situations on their own, I would always have one set of clothes on hand for each. Sometimes a dry pair of socks, or a fresh shirt make all the difference for comfort on an active day.