Just as an exercise, I ran a test - worked fine:
Sub threeDBcopy()
Dim objAcc As Access.Application
Dim DB2_Name$, tableInDB2$
Dim DB3_Name$, tableInDB3$
Set objAcc = CreateObject("Access.Application.9")
DB2_Name$ = "F:\DbData2000\xxxx.mdb"
DB3_Name$ = "F:\DbData2000\yyyy.mdb"
tableInDB2$ = "Works Order"
tableInDB3$ = "Works Order"
objAcc.OpenCurrentDatabase DB2_Name$
objAcc.DoCmd.TransferDatabase acExport, "Microsoft Access", DB3_Name$,
acTable, tableInDB2$, tableInDB3$
objAcc.Quit
Set objAcc = Nothing
End Sub