I have not tested this, but here is something you can try... Let's say that you have D:\Data that you have shared as Data. Change the share permissions to remove access to Peter. If the share permissions use a general name like Everyone or Domain Users, you would need to add a DENY acl to prevent Peter from accessing the share. Generally, I don't like using DENY acl's, it would be better to grant access to the user's groups that do not include Peter.
The create a second share on D:\Data and name if Data-Peter. Or Data-Peter$ if you want to hide the name from other users. In the permissions, set it so that only Peter can access the share. Set the allowed number of users to 1.
See if that stops the second PC from accessing Data-Peter.
You may run into timing issues that you will need to test. For example, If Peter maps the drive and sets it to automatically remap every time he logs on, does that count aa the "1 user" or does Peter have to access a file on the share first.. Also after a period of inactivity, does the server disconnect the "first Peter" which would then allow the second pc to connect.
This looks very much like an XY Problem. If the Peter account is allowed to access the share, why do you need to restrict it to one PC at a time?