Simple solution really is to not use the built-in DNS shim in the DSL router or a Vz DNS server. You should be able to go into the configuration setting for you router and find the DHCP section -- there, try changing the DNS settings from "dynamically assigned" to "these servers" and try one of the many public DNS servers like Googles: 126.96.36.199 and 188.8.131.52
Not all routers let you give out your own DNS and instead supply the local shim on the router -- which is likely what is crashing on you (and thus using your own router could help there).
To test this theory, on any device where you are expiriencing this, you can also change their configuration to specify the DNS servers you want instead of the ones that the DHCP server gives you. Same deal as above ... use Google's or one of the other many public servers and see if that fixes you up. Not ideal, but it will pinpoint the router as the issue.