二枚重ねてはいけませんって英語でなんて言うの？

This is a simple way of saying it.

The machine will not read your card if there are others with it.
When we scan a card or ticket, the machine reads the details. If there are other cards overlapping, the machine cannot read the required card which will result in an error.
A simpler and more direct instruction is this
– “Make sure to use the card separately or the machine will not read it.” This clearly tells the person to keep the card away from others.

An error is when a machine does not do something properly, for something to happen or for it to do something this is called 'to occur' you can simply say 'the machine can only read one card at a time'

It seems here's the main problem is that people are not separating their cards properly and this point needs to be emphasised to them:
"Sorry, but my card isn't working."
"If you have two cards close together, the machine will show an error."
"OK, thanks!"

▪You should only use one card otherwise the machine will malfunction.
malfunction=a failure to function normally

▪Errors will pop-up from the machine when more than one card is being used at the same time.
pop-up= message block that will appear on the screen.

Both the above sentences clearly indicate that the machine will encounter a error when more than one card is being used.

"An error occurs if you try to touch more than one card at a time."
This explains to the person that if they try to touch two cards at the same time it will make an error.

"If you have two cards overlapping it will cause an error."
This explains that if two cards are overlapping the machine will show an error.

A proximity card = A "contactless" smart card which can be read without inserting it into a reader device. They are a part of the contactless card technology .
Magnetic stripe cards = such as credit cards and "contact" type smart cards.