Use the run box (windows key +r). Enter a command (like cmd). hold ctrl+shift keys and press enter. Alt + y to accept the UAC prompt. Elevated command prompt in 10 key strokes.
If you put a batch file in a folder on your systems PATH you can execute it directly from the run box. Eg create c:\windows\mycoolscript.bat, and from the run box just enter mycoolscript (a better idea is to modify the path to include the folder where you scripts live - either works)
To add a user to a group look at the net command:- https://docs.microsoft.com/en-us/previous-versions/windows/it-pro/windows-server-2012-r2-and-2012/cc754051(v%3Dws.11)
Updated following comments...
If you want an unprivileged user to run privileged commands from a script you need to provide them credentials, or have a more privileged account execute the script on the users behalf.
Providing credentials - PowerShell can generate "SecureStrings", and you can store a representation of that object in a file and reload it later so you could . In theory the file can only be read back on that machine, but it uses reversible encryption so its not really that secure - but its easy and might be good enough? Eg https://4sysops.com/archives/encrypt-a-password-with-powershell/
Another option is to take advantage of Windows Task Scheduler - setup your ps2 script with an account with whatever rights the script requires and a trigger based on a Windows Event Log event. This allows your unprivileged ps1 user to write a message to the Windows Event Log (using custom event id), and have your ps2 script be executed in response to that custom id under different credentials. This is more secure, but theres quite a bit more work involved.