The last guy I personally knew who regularly did anything like this passed away several years ago. During many conversations over adult beverages he shared stories with me about the 4 to 6 weeks he spent every year in the Colorado high country. From what he shared with me I understand that placer gold is fairly common, but usually in such small quantities that the return cannot justify the time and effort of panning. Also, it is very hard work, way beyond physically challenging, more into the realm of damaging to the human body.
The method that he described involved digging up bank areas and sand bars in streams, transferring the sediment collected in those spots to a sluice box. His sluice box (which I have seen) was about 2 feet wide by 6 feet long, equipped with small pontoons so it floated, and was powered by a small gasoline engine that kept up a steady rocking motioning back and forth to settle out the heavier elements into a container for later processing. This allowed him to move all of his equipment in the back of a pickup truck, requiring only an hour or so of set-up or break-down time, so he could work multiple spots depending on where "color" was showing up (he knew dozens of places that were worth working each year, as sediments are regularly carried downstream during spring run-offs). The gentleman was a large and powerful man, so he usually did everything by himself, but he did mention several times that he wished he could find a trustworthy helper to go along on those annual working trips (he was well into his 70's by then, so the physical aspects of his "hobby" were becoming a problem).
He talked about potential problems involved such as possibly trespassing on private property, working claims held by others, and legal problems involved with working on federal or state park lands and national forests (Colorado is about 60% public land, state and federal combined, and there are volumes of laws dealing with such matters). His approach was pretty simple: get in and out quickly, and if he were ever approached or questioned he would just play the dumb old retired guy with a quirky hobby. I don't recall that he ever mentioned any such confrontations, but I know that he kept a loaded shotgun and loaded rifle (Mini-14) close at hand.
Bottom line, every year his 4 to 6 weeks of work usually netted him between $10,000 and $20,000. Placer gold (dust) was sold to a foundry, paid at the rate of about 90% of spot value. Nuggets were sold to custom jewelers specializing in nugget-themed jewelry, and nugget value was actually higher than the spot value of gold content.
Based upon what that old boy shared with me I would suggest that you and your son could have some fun together, and perhaps come back with enough gold to pay for your vacation together. I would not mount an expedition based on expectations of getting rich.
Then there was another guy I knew who mined for gold. He worked in a mortuary, the mining he did was based on extracting gold dental work and jewelry from the dearly departed, working quickly between final services and final rest. It took a few months to build the case, and a year or so before the trial was concluded, but his net gain was 4 to 8 years in a prison cell. I guess everybody needs a hobby, but some are less attractive than others.
