WiFi from fiber optic modem+router freezes computers. Bizarre mystery. Fix?

I am experiencing a very strange problem and can find no way to fix it. I'll try to explain it as clearly as possible.

I just had a fiber optic cable installed at my home ("Sonic Gigabit Fiber"), which terminates in a modem which converts the fiber-optic signal to a high-speed broadband Internet connection. This modem is then connected to a wifi router (via a Cat5-E ethernet cable), and the router then puts out a wifi network. When any of my computers (running OS 10.6.8) connects to this wifi network, they freeze up within about 15 seconds -- the Finder freezes, mouse/trackpad/keyboard become unresponsive, etc., and the only way to unfreeze them is to physically turn them off by pressing and holding the power button.

Simultaneously, I still have my previous Internet service connected -- a standard Internet signal from Comcast/Xfinity arriving via a coaxial cable, which then also terminates in a standard modem. But here's the crazy part: When I plug the exact same wifi router into this modem, and then try to connect the exact same computers to the wifi network it creates -- they connect with no problem whatsoever: no freezes, everything fine!

How can this possibly be happening? I was informed by tech support at both Sonic and Comcast that there's simply no way that a wifi signal, whatever its source, could possibly cause an operating system to freeze. And yet -- it does. Which is why I'm asking here, since the companies involved have no idea as to the source of the problem nor how to fix it.

This happens when testing with either of two different wifi routers: AirPort Extreme, and a new Zyxel.

And it happens consistently every single time it is tested: When the Sonic fiber optic modem is connected to either router, ALL my computers will freeze, every time; yet when the Xfinity coaxial cable modem is connected to the same routers, nothing freezes and everything works fine.

Note also that all the computers do indeed detect and successfully connect to the Sonic wifi signal -- its just that the act of connecting to it is what freezes them.

Here's the best clue as to what the issue might be:

When the technician was here installing the fiber optic cable and modem, he tested it on his computer -- a MacBook Air running OS 10.9.2 -- and the wifi signal did NOT freeze his computer. So the issue, it seems, is some conflict between a wifi signal which originates from a fiber optic gigabit modem connecting to a computer running Apple OS 10.6.8 specifically. Because the issue does not exist with a computer running a later operating system, nor does it exist with a modem getting its signal from a standard copper-wire coaxial cable.

And yes, I know that one solution would be "Get a new computer," but what I'm asking is how I can fix the problem keeping the computers I currently own with the OS they currently have.

Here are the specifics of the hardware, in case it's relevant:

Computers, all running Mac OS 10.6.8:

MacBook Pro (model 6,2, 2010)

MacBook Air (model 3,1, 2010)

iMac (Intel plastic, 2006)

Modems:

Sonic house-brand fiber-optic modem (no model number visible) (2019)

Arris/Xfinity TG862 (2015-ish)

Routers

Apple AirPort Extreme Model A1143 MB053LL/A, 802.11a/b/g/n* (2007) running firmware v.7.6.9 (the latest available for this model).

Zyxel P-660HN-51 IEEE 802.11n (recent)

The service provider for the fiber optic connection said they are running IPv4, not IPv6.

The computer that didn't freeze up was a

MacBook Air (model 5,2, 2012) running Mac OS 10.9.2

Sorry if much of this info is irrelevant -- just wanted to be thorough with the question.

Does anybody have a clue as to why this is happening, and what can be done to fix it? Thanks.