There's at least two ways to set up a dual boot. One is the way Draclvr did it -- where you install with both the new drive and the Windows 7 drive attached. Windows 10 will see an earlier Windows version and provide you with a boot menu. Be careful that Windows 10 installs on the correct drive and doesn't overwrite Windows 7.
Another way is to disconnect the Windows 7 drive while you're installing Windows 10 on the other drive. The advantage of this method is that there's no danger of installing Windows 10 on the wrong drive and overwriting your Windows 7 by accident. If you do it this 2nd way, you may have to choose which version of Windows to boot from by going into the BIOS (or UEFI) settings and adjusting the boot order (which hard drive to boot from) whenever you want to boot to the other Windows.
When you install Windows from a DVD, you have to set the boot order in the BIOS (or UEFI) settings to boot from the DVD. You know how Windows reboots during the installation? Once it's installed enough of itself onto the hard drive and wants to reboot, having computer set to boot from the DVD may give you a menu to boot from either the DVD or the hard drive. You'll want your boot order set so the 2nd boot device is the drive Windows 10 is installing on, not the drive Windows 7 is on. Once the installation is complete, you can remove the DVD drive from being first in the boot order.
Is there a way to pick which drive you want while the computer is on and just switch from one to the other?
You'd have to reboot to get to the other one. Whether you have a boot menu or whether you go into the BIOS (UEFI) to change the boot order to use the other hard drive depends on how you installed.