... large number of refurbished routers available
... I don't see huge qtys of refurbed motherboards.
Router is a separate box. Practically everyone has one. Easy to take back.
Motherboards, yes, essentially every device has one, but does one eagerly disassemble (OEM) computers to get refurbish a board?
... general crap construction.
That.
They are build, tested, sold. They bounce back (for whatever reason) and are retested and (potentially) resold.
Does a test reveal all defects? Hopefully yes, probably no. New and refurbished are no different in that matter.
Refurbished has (perhaps) seen some action and thus should not be dead-on-arrival like the new could be.
On the other hand the refurbished has already worn in use somewhat.
New or used, a cheap is cheap, through and through.
In the case of OP there are one or two subnets, LAN, in the premises.
There must be a router.
There must be VPN. (Assuming a client that connects to an external VPN server.)
There must be at least one wireless access point (AP).
If only one device will use VPN, it could be a VPN client itself. Otherwise, it is more logical to run VPN on the router.
If the router has VPN, it can direct some traffic via the VPN tunnel and other traffic outside the tunnel.
One LAN and everybody is connected.
Alternatively, traffic of one LAN goes via tunnel and the other LAN's outside of tunnel.
Its just a bit different ruleset on the router (assuming the router can be configured).
If there are two LANs, the members of each must be connected somehow. Either separate physical (wires/wireless) network for each LAN, or VLANs.
In VLAN more than one logical subnet uses common wire. Wire that is between router and AP, router and switch*, switch and AP, etc.
VLAN is simply a way implement multiple logical subnets without building multiple physical networks.
(*managed switch)
Routing with NAT needs some computation power. VPN needs much more.
The cheap multifunction devices (usually called "routers") can have router, VPN, VLAN, and AP in one box. They may or may not be powerful enough. They may or may not be sufficiently configurable. They may or may not have pleasant TCO.