I know this isn't the most pleasant thing but our life saver during potty training was a portable potty with disposable liners. IT folds flat and you pull out the legs and have in it a little liner which has a pad on the bottom to absorb liquid. The child sits on it - wees - and then you just tie up the bag and pop it in a bin. Or put in a nappy sack (just in case!) and keep it till you are next to a bin.
I know its not great to do in a line but there may be situations where it may be needed. Actually if you have bags to put down by you and use it very discreetly most people don't even notice you are using it.
Rather than get out of the line for a ride, have your child use a portable potty! No one will notice or even care that a half-naked kid is peeing in the line!
And thankfully, other people are like, "What?", so the poster comes back with:
Are you serisously telling me that you would never use a travel potty in public?
That's not what they're for! You're in a theme park with restrooms every few meters. Get out of the damn line and act like civilized human beings.
The poster eventually flounced when people thought using a potty in line was way gross and inappropriate, but yeah. What the hell is wrong with people?