Is it possible to prevent certain PC's from using a specific router?

I think we need to know a bit about your setup. If the phones and PCs eventually go the same router , and you have multiple internet connections on the router, you could put the PCs in a different ip network and use a route-map to do source based routing (if your router is a cisco device, although other routers can do that too).

If you have different routers, just set the default gateway on the PCs to use the router you want them to use. And if you really want to be sure, put an Access Control List on the phone router not to allow traffic from the PC network.

If you don't need any communcation between the "phone network" and the "PC network" just put the client devices and their servers/routers in different VLANs and be done with it.

In your dupe question you mention prioritization of traffic. Unless you've got serious amounts of traffic you'll be able to get by fine on a small network running 100Mb or gigabit Ethernet w/o any prioritization of VoIP traffic. When you get into lower bandwidth links, or high network bandwidth utilization overall, you'll start to need to worry about prioritization.

Edit:

If you need communication between the networks you're going to need a router with interfaces in both VLANs, then.

It could be a layer 3 entity on an Ethernet switch (if you have at least one layer 3 capable switch), or it could be one of your edge routers.

Keeping the phones and phone servers using their own Internet connection and the PC's using theirs is really pretty easy-- that only depends on having the right default gateway set on those devices.

Each edge router should also have a static route to the "other network" (via whatever router you decide to route between the networks with) and then you'll have communication between the VLANs.

What is the reasoning behind having any shared network resources? My first instinct would be to put the phones and the computers on completely separate networks, then you don't have to worry about prioritization because they don't compete for any resources and there is no way they can go out through the wrong router. If you need them on the same network for some reason then the trick is going to be to make sure that they have different default routes. Phones should have a default route through the phone router, computers should have a default route through the computer router. You can do this by statically assigning routers, or by using DHCP groups to hand out the right configs to the right devices.