There isn't quite enough info your your diagram for me to figure everything out.
The Cisco 3750 is being replaced by a Cisco 2951, or is the Cisco 3750 being retained? If the Cisco 3750 is going, move it's IP address onto the Cisco 2951. Then everyone can maintain their current IP addressing, and since they are going via the 2951 will start using the new Internet circuit.
If the Cisco 3750 is staying, then connect it and the Cisco 2951 together, and change the default route on the Cisco 3750 to point to the Cisco 2951.