I did a little research and was able to add the drivers needed to the Adaware Rescue USB. Here are the steps if someone else ever needs to do this:
1. Download the new drivers. In my case they are in 25_0.zip from https://downloadcenter.intel.com/download/22283/Intel-Ethernet-Adapter-Complete-Driver-Pack
2. Unzip to folder, say C:\25_0
3. Create a folder on your drive to mount the Adaware boot image, in my case C:\AdAwareImg
3. Mount Adaware Rescue USB. In my case as J:
4. Mount the WinPE boot image:
5. Install the new Intel drivers:
6.Unmount and save the Windows PE image:
Now when I boot from the Rescue USB I am able to reinitialize the network adapter (under Advanced options) and update definitions. For some reason, sometimes I need to click on "Initialize adapter" a second time before it works.