When you say 3DNS, are you actually referring to GTM (or BigIP DNS), or are you still running version 4 code ?
The clients are going to make DNS requests to the GTM for the IP address of the virtual they need to connect to. There's persistence that can be applied to the WideIP pool settings, but what that's doing is persisting the same answer back to the same local DNS server. If you clients are making DNS requests that are hitting the GTM from more than one local DNS server, then they could be given different results.
The cookie persistence doesn't really come into it - that's only going to be presented to the pool member once the data centre (the wideip name resolution) has already been selected.