Worth a try but often setting a static speed on a decent switch when communicating with a cheap router can cause just as much aggro. Really we need the specs of the Virgin hub to be absolutely sure of the speed of the yellow switch ports on the hub. It may be that there is something going on with the managed switch "confusing" the hub with all the "extra" traffic a managed switch generates (not that much, but it isn't silent) so adding an unmanaged switch in theory would not help as it will simply forward all the same traffic to the hub. But it's worth a try...
With regards to wireless, irrespective of what type of extender is added to the system, go in to the settings of the extender, change the wifi name and password to match what is normally used and it will work seamlessly. No need for different network names everywhere.
With regards to wifi signal itself, 99.9% of issues of "bad wifi" I respond to and resolve have NOTHING to do with the network equipment and EVERYTHING to do with the device the user has in their hands, IE the phone or tablet. Here's the tech, and I'll try and keep it short and simple...
A wifi network is a two way HALF-DUPLEX radio network. Half duplex means if one device is talking the others are not. I'll come back to that.
The signal from the router/hub/extender/access point or whatever is in use to broadcast the wifi signal, must be strong enough to reach the user device and provide connectivity.
The user device MUST be able to provide a signal strong enough to broadcast its traffic back to the router/hub/extender/access point or whatever.
It is the user device that is usually deficient NOT the ISP supplied equipment. At full power, a router/hub/extender/access point will push out a signal strength of 100Mw (100 milliwatts, or 1/10th of 1 watt). No, it won't go through thick walls...
A phone or tablet often maxes out at HALF to three quarters of that strength. Having a "more powerful router" is often not possible because maximum power is regulated by law so don't be fooled by marketing garbage about "strongest signal in theUK" 'cos they all are... it's how they are deployed that's key.
If the "problem" is that the wifi signal showing on the phone is only (lets say) 3 bars out of 5, (or 2 out of 3 on an iPhone) if you measured the user device signal at the router, it would be LESS than that. The wifi can reach the user device fine. But the user device can't reach back well enough to provide speed or reliability. 99.9% of the time this is the problem.
HALF-DUPLEX. Like a two way radio, if your device (phone/tablet/laptop) is "talking to" the router, then the router is listening. If the router is talking to the device then the device is listening. ALL wifi devices cycle through this Tx/Rx process VERY quickly so it looks like the device is working seamlessly, but it isn't.
And remember that once a page is viewable on the device, you're not really on the internet. The page has been sent in it's entirety to the device. It's only when you click to go to the next page or click a link that the Tx/Rx process happens again so the device is largely "silent" in use when browsing the internet.
I could go on and on, but I won't. There's a whole world of wifi "optimisation" that can happen, but in all of that please remember that when the problem is wifi, it's usually (that's USUALLY) NOT the network... there are exceptions of course but in my experience they are rare.
Lastly a wifi mesh network is one where the access points can "see" multiple other access points so they have failover paths should an access point fail. In a house or at the office where there are access points in rooms that connect with wires back to a central switch / router for internet connectivity, they are just wirless LAN's, not "mesh" networks... usually...