Get a car potty.
Via Amazon, do a search for "on the go potty" or "travel potty."
We have one and so do ALL of my friends.
It is a life saver.
And stock the car with extra clothing and undies and/or diapers etc.
And toilet paper.
A child, no matter how old, will have accidents.
And your child is only 3.
And during traffic or in places without a toilet, or at parks... then what??
Therefore, a car potty, is REALLY great.
We still use ours. And our kids are 5 and 9.
I took my kids out in undies, ONCE I KNEW they were ready for it.
These things goes in stages.
And then just short outings at first.
And explaining to them and our telling them that they CAN tell us, no matter what, if they have to pee/poop, and do not be afraid of making mistakes. They are only learning now. Its okay to make mistakes. ALL kids do.
My routine was:
undies at home
Once they mastered that, then, we went out with undies. For short outings. Until they mastered that, it was diapers while out.
It goes in stages.
I EXPLAINED that to my kids.
Thus they did NOT get "confused" about being in diapers or undies nor did they regress or back track in their progress.