@EagleGC You have to have the Procurve switch plugged into the SG-1100 LAN network, which it looks like it already is. Then, the Nest wifi router should be in access point mode, then plugged into a switch port on the Procurve switch. This process will put them all on the same notwork.
The Procurve shouldn't "hand out" any IP addresses, you should set it up to NOT offer up IP addresses. Unless, you've got a special reason to do that.
Jeff