Servo as a door lock, How can I ignore a button until later in the program?

[Grumpy_Mike]

But the main issue is how to temporarily ignore button 2 until after button 1 has
been pressed

Get button 1 to set a flag, nothing else.
When you see button 2 being pressed, look to see if the button 1 flag is set, if so do the stuff you need and reset the flag.