It appears from your description that there are two 2960 switches that are connected via a trunk interface. A device is connected to switch 1 and the you are seeing packets that match the QoS policy on that device's input interface. Between Switch 1 and switch 2 there is a trunk interface. On the incoming trunk interface on Switch 2, the same QoS policy shows no matches.
First of all I would not be rechecking and resetting the packets on Switch 2 as they enter from Switch 1 (maybe you are not doing that).
But you do need a command on both switches' trunk link that will trust the incoming DSCP value because, depending upon the IOS version I think, the default state is to reset the COS to 0. In Ver 15, this is "mls qos trust dscp"
Assuming you have a separate router at each site, this command should also be on the interface to the site router so that incoming packets are not reset. You will also need to set this on the 3560 switch interface which connects to that site's router.
If the sites are directly connected via the switches (i.e. no router), put this command on the connection interface of both switches.
If this doesn't help, post the configurations, a diagram and the results of the show policy-map interface commands