In theory you could use the TP-LINK you bought but it's all slightly more difficult to do that you might have thought. Firstly there is no adapter and you can't replace the VM hub, you have to use both together. Basically you put the VM hub into 'modem mode' which disables the router and wifi features leaving just the cable modem part working.
A admittedly, very brief reading through the specs of the device you have purchased claims that it has a WAN ethernet port (I believe it uses one of the LAN ports for this), so you connect an ethernet cable from one of the ports on the VM hub (making sure that it is the one and only ethernet cable connected to it), connect the other end into the WAN port of your new router and configure it accordingly.
If you check through the Networking section of this forums, there are a couple of posts scattered around describing how to put the hub into modem mode and the somewhat counter intuitive order of which need to be power on first.
I do have to say though, that the device you bought isn't particularly good, and if you have one of the faster internet connections from VM, then it is likely to be a bottleneck in itself.
I'm sure your son will be able to get it all working though.😉