Potty training at home is one problem. Potty training in a park, a mall, or the back of a car is a completely different one, and it is the part most guides skip.
Children in the middle of training do not give you much notice. That is not a failure of training, it is just how it works at that age. Planning around it works far better than trying to rush the timeline.
Consistency matters more than location. Whatever routine you have built at home is worth carrying with you, even when the setting is odd. The familiar sequence is what keeps a child calm somewhere unfamiliar.
Accidents outside the house feel worse than they are, mostly because of the audience. Having a plan for them removes almost all of that pressure, and a calm parent makes for a calm child.
Most importantly, do not let the fear of an accident keep you indoors. Getting out is good for both of you, and being prepared is what makes it possible.