Theres an easy way to drain the tank, if thats what you decide to do.
On the bottom of the carb float bowl, there a hose, and a screw which opens a valve. Put the hose in a gas can, unscrew that screw, a few turns( dont unscrew it all the way), and turn the gas tank valve to either pri or if it doesnt have a pri position, then use res. That should drain the gas tank almost empty...add new gas and its good as new.
Hey things happen...dont be afraid to tell dad, this isnt a biggie. The tranny stuck in 5th is totally unrelated to the gas. If you rock the quad front and back, while shifting, it should make it back to neutral. Atv trannys need wheel motion to shift reliably.

 

Let me elaborate a bit more. Boat gas, meaning gas that has been mixed with a good 2 stroke oil, is not in any way harmful to a four stroke ATV. If the ATV in question is a 2 stroke then it probably has an injector system for its oil and doesn't need a 'premix' gas. None the less, your mixed boat gas will not present any problem. It will be consumed without noticable smoke. Formulations at the proportion needed these days, usually about 50-1 pose no problem at all in assimulation. If the quad is a four stroke, no problem still. I doubt any smoke will be detectible. In fact some reccommend that 'top oil' meaning essentially 2 stroke oil, be added to the gas for four strokes normally. The mixed gas will make no difference at all. let it go through. You will never know it was there. If dad freaks out, he just doesn't understand motors. The kid did no harm. Rock the quad shut off to free the shifter. Don't worry about it. All is well.

 

Mixed gas, is actually leaner than pure gas, due to the oil content. If this is a two stoke, that could end up being harmfull,If the motor was borderline, lean running., and has oil injection. The best thing to do is tell dad, your son didnt mean to cause harm, and if something bad does happen, hes gonna be upset you couldnt or didnt tell him right away.
Ive told my wife and girls to let me know as soon as they know theres a problem. Whether they caused it or not. Its about respect, it was dads money that bought it, itll be dads money to fix it, it should be dads decision on how to procede.

 

It is a Honda. Thanks guys for all the replies. Doesn't sound as severe as I thought it was! I thought he had locked up the engine! Good to hear it was nothing major. Thanks again