If it still has the stock petcock, that is the most likely problem.

Dry everything out, check your oil. If it's dumping gas then it's likely in the oil.
Get an Official Yamaha Raptor petcock. No cheap knockoff. They have smaller diameter plumbing and don't deliver fuel well. Someone here will come along and give you the part number, hopefully.
The fuel line from petcock to carburetor shouldn't keep running if you disconnect it.
Unless Someone accidentally set the petcock to Prime.
Even then, the carburetor shouldn't let gas keep going. The needle and float Should stop the gas from leaving the bowl unless it's running.

Welcome to the World of Problems you never saw before you got into motorcycles.
It's a learning curve, but if you're patient and determined, you and your son will have a good time and learn a buncha new stuff. There are guys here who can help you with whatever you're fighting.

You can use a screwdriver handle and give the carburetor a quick Rap or two. The float might just be stuck a little.
If the petcock has an Off position, put it there. I haven't had one in so long I don't remember.

When you change oil, don't use the fancy stuff with friction modifiers. The clutch will slip. The guys who have 100,000+ miles run Rotella. Usually available at Tractor Supply.
It's NOT impossible to get the oil filter in backwards. It's usually fatal for the engine.
So, don't Do that!!
You can build a shield from foil to guide the oil down from the filter and keep it off the header.
Let the air filter air dry if it's wet.