Are the IP phones connected to the system at site 1 or are they stand alone / SIP phones? If they are IP sets off the system your problem may not be the T but the connection between sites.... and a good wireless connection might help.

Are the digital sets experiencing issues as well? ... that would point to issues with the T.

Seems to me if the telco is going to sell you a T then it should be willing to insure that it works.