There is a free Windows utility that should be able to get the job done called QRes. You can use the CMD to change to any of the supported resolutions, therefore you will be able to create a .bat file to switch between the two resolutions:
Once Qres is installed do the following to create a simple .bat file:
1 - Open notepad, create a new file and copy and paste the following command::
%homepath%\Downloads\QRes\QRes.exe /x:1920 /y:1080
In the command above make sure to enter the correct path for the QRes.exe file, and enter a supported width (x) and height (y) pixel resolution. For example, 1366 x 768, 1440 x 900, 1680 x 1050, 1920 x 1080, 2560 x 1440, etc.
2 - Click the File menu and select the 'Save A's option.
3 - Save the batch file with a descriptive name and a .bat file extension.
After you complete the steps, double-click the batch file and the screen resolution should change automatically without the need for extra steps. You can create a second batch file with the alternative resolution and switch between the two resolutions with each separate batch file, or if you need to change the display resolution constantly then you could write something with a toggle using Autohotkey:
An example of an AutoHotKey script in conjunction with Qres might look something like this:
#a::
toggle += 1 ; This increments toggle state (so values after execution of this line will be either 0 or 1)
if (toggle = 0)
{
Run %homepath%\Downloads\QRes\QRes.exe /x:3840 /y:2160
}
else if (toggle = 1)
{
Run %homepath%\Downloads\QRes\QRes.exe /x:1920 /y:1080
toggle := -1 ; set to -1 so on next run it will end up being 0
}
Return
This script would use Windows A Windows+A but could be changed to whatever you like (preferably something that Windows doesnt already use). Again, the path to Qres would need to be inputted to the correct path.
There is more documentation on the use of Qres here. (some source of this question from that site).
Alternatively, you could use the freeware tool NirCmd. Example of usage:
nircmd.exe setdisplay 1920 1080 24
This changes the display to a resolution of 1920 x 1080 with a 24 bit color depth. You could use NirCmd in conjuction with AutoHotKey as shown above to have a functioning toggle.
There are a lot of good solutions on Super User in this question as well, but I think what I have provided will suffice.