I have to ask...
1/ How do you know it is dog piss? Foxes would probably piss at night (dawn and dusk) but cats will piss on car tyres at any time and are particularly fond of cars as 'territory markers', lurking under them often all day long in drawn out battles of 'Cat Chess'...
2/ How do you know your child is severely allergic to specific animal piss, was this tested for, are they only allergic to dog piss, what about fox piss, cat piss, badger piss, otter piss, etc etc (cat, dog, otter, fox, badger, deer, mink, rat - all common sorts of piss where I live and yes urban otters are a thing here!).
3/ How is your child contacting this allergen - do they hug your car tyres, lick them, can you not stop them touching the wheels/wheel arches?
I discourage/prevent my dogs pissing on peoples stuff, and carry a squirty drink bottle of water when walking them (for drinking but also emergency 'sloosh down piss' purposes) but I also take the view if you leave stuff out in public where the public have access to it, where wildlife has access to it, you have to accept you give up control to some degree as to what happens to that stuff.