Put the barge "on the hip," that is alongside the tug. Place the tug well aft, with its stern aft of the barge's stern. Angle the stern of the tug out from the barge 20 degrees or so. Or make the tug up at the stern of the barge on the centerline, to push it. Make all lines bar taut, so the tug and the barge move as one. Both of these methods give much better control.