Can a differential probe and regular coax wire be connected safely to only one channel of scope using a tee connector?
Yes, it can be damaged or at least it will interfere with the DUT1 measuring. The differential probe has an operational amplifier at its end - coax driver THS3202 or similar opamp. It is intended to drive a coax with a load of 1M ohm an 20pF, not a voltage source. If you connect the voltage source at its output it could be damaged