Apple ID issue with secondary imac

i bought a used imac to have a computer while i was visiting my family in france and it was also going to be used by a family member for a secondary Mac. i set it up using my Apple id.

Suddenly she has been locked out and we are having issues with logging in.

it asks for log in for the Apple id then asking for computer login then asking for

Log in I use on my Mac which is main computer linked to Apple id. It just seems to going round in circles and my sister has in the confusion put the wrong one in a couple of times and now it is saying this.

Not sure what to do at this point with our losing all the data apps etc on the Mac