You make it sound like an epic breach of security is taking place. It really isn't. You're making this all much more dramatic than it is. First, if anyone was "hacking" into your router (whatever that means) it would not mean that your computer is being compromised in any way. I mean really? What can someone do if they can control your router settings? That in no possible way means that they have done anything to your computer. Absolutely Zero. And even if this was the case, then simply change your WiFi password and/or encryption (i.e. change WEP to WPA)!
Second, if all of this is happening with a specific program (or at least began that way) then it is that specific program that is the problem. You also mentioned when the firewalls are turned off that everything works out fine. Bingo. Not sure what the issue is still.
If anything you can do a hard reset of the router but that will get rid of all of your settings on the router. Or just try using this program without the router at all (plug your MBP directly into the internet modem). If that works then again, its something screwy with your router. Your situation does not sound like anything malicious is happening but rather just some hardware glitch with your router. This stuff happens. But I am still about 99.9% sure this has nothing to do with spyware/virus/hackers/KGB/FBI/CIA* or any other crazy things that you may be scaring yourself over. That sort of stuff is only in the movies.
*Unless of course you are an international spy that has the top secret micro-fiche.
