National Rail website gives it (I used via W'hampton)
Only if you go for more restrictive tickets, I think. There are no day returns between Wrexham and Derby (or day singles, for that matter), so anyone taking a day trip will benefit from splitting. I'm not sure there are any splits via Birmingham if you don't go that way.... and tells you that you need to buy more than one ticket for the journey.
This, of course, neatly undercuts the overpriced through fare (priced by CrossCountry and which it thinks is invalid) by splitting fares at Birmingham and even offering advance fares which don't exist on the through ticket.
Via Birmingham and Shrewsbury is valid on maps CE+BC in the routeing guide.
However, booking engines won't give you itineraries this way since the route has been removed from the electronic version of the routeing guide. I believe this is another example of an attempt to remove a reasonable route by stealth.
... and tells you that you need to buy more than one ticket for the journey.
This, of course, neatly undercuts the overpriced through fare (priced by CrossCountry and which it thinks is invalid) by splitting fares at Birmingham and even offering advance fares which don't exist on the through ticket.