You have two location/buildings. One has internet and the other does not.
If all you are trying to do is link the two sites together then you can forgo the MX at the second location. Simply trunk the core switches and create the shared vlans.
If you wish to keep the separate you could use the MX with internet to service both site by connecting the site cores directly to the MX and use diff vlans in each site and L3 firewall rules to segregate traffic.