Once you copy everything you want to the 2nd hard drive, disconnect it. That way nothing can affect it in any way.
Once the factory restore is complete, reconnect the 2nd drive and you should be all set.
Is there anything on the 2nd drive now? If not, you might want to do an image backup of the 1st HDD to the 2nd HDD rather than just copying some files. That way you won't forget anything, it will all be there and if something goes wrong during the factory restore, you can restore the backup image to the the 1st HDD and you will be right back where you are now.
I recommend using Macrium Reflect Free for this. Once installed, create the rescue disc or flash drive so if necessary you can restore the backup image you will create.
Good Macrium tutorial by whs here: Imaging with free Macrium