I remember a cartoon
I remember a cartoon from many years ago when the whole V-Chip thing was basically brand new. The cartoon was of a guy setting the password on one of these things, and the caption was along the lines of "Another 30 second challenge for your kid."
Also, creating a custom router firmware is not as easy as you'd think. With maybe a very few exceptions, the companies that make the router hardware don't tend to give out the information you'd need to make that firmware. Then even assuming you base it off of say Tomato or DD-WRT, what happens if the version it was based off of ends up having a major security hole in it? Or even more basic, what happens if you, the parent, forgets the administrative password and you paid someone to remove that? More than that, what's stopping the kid from just pulling the cable from the DSL or Cable modem into the computer directly? Or maybe they go out, buy a router of the same make and model as the router you have, configure the same SSID, WPA password, etc, only now THEY are the ones with the admin password to the router. Or less cloak and dagger-like, they could just get a small router and just yank the WAN feed when they want to use the Internet.
Then if we go back to the programmer idea... Those people are probably going to charge $100-$200/hr, and if the OP has that kind of money, they would probably be better off spending it on a therapist to actually try and deal with the problem, not play a game of whack-a-mole with your kid. No matter how clever you think you are, they're more so. Harsh reality of aging, is that after about 30 or so, it's downhill for your cognitive functions. Not to mention your kids have grown up around this kind of technology, so it's second nature to them, whereas you have to stop and try and figure things out. Hand a 10 year old a cell phone and they'll take to it like it's nothing, whereas you hand someone who's 50-60 (or older) that same cell phone, and odds are it's going to take them significantly longer to work things out. That's just biology. You don't have to like it, but it's happening as we speak. Neurons are dying and are slower to regenerate every day for you, while someone who's under 25 is generating them at a faster rate than they're dying (barring things like heavy drinking, head trauma, etc).
At the risk of someone thinking it's a personal attack, there are holes in your ideas large enough to sail a small navy through. The only real solution, and it's not really a solution, would be to stop all Internet service and get rid of the computer. However, that would have a crippling effect on the job prospects of the OP's son.
At the end of the day, the OP has a social problem, and those cannot be solved by technological means.