A Flight Instructor reported their aircraft's right brakes malfunctioned due to a hydraulic fluid leak and they had to be towed to parking after landing.

Narrative

On day 0; at approximately XA:05PM; during a routine training flight at ZZZ1 and just shortly after takeoff; I noticed that my right-hand brake pedal was feeling spongy. Didn't think of it much; however within a few seconds I started to smell hydraulic fluid and notice a puddle of hydraulic fluid below my rudder pedals. I asked my student to test his brakes on his side and he mentioned that he also feels that the right rudder pedal feels spongy compared to the left rudder pedal. When he mentioned that; I tested it again and found that I have no control of the right hand brake. My student wasn't sure about his brake system on his side and the smell of the hydraulic fluid was getting stronger. Since we were already in the air and originally flying back to ZZZ; I decided to continue the flight to ZZZ due to Tower service; assistance; and longer runway. Once I was approaching close to ZZZ's Class D airspace; I obtained weather and contacted Tower requesting landing at the airport. The Tower cleared me to proceed to the Building then left base for Runway XXL. I also informed her that I smelled hydraulic fluid inside the cockpit and told her that I think I may not have the right brakes. She acknowledged my transmission and asked if I am [requesting priority handling]. I replied affirmative and gave me the necessary assistance needed for the situation. She allowed me to proceed to Runway XY after she stated winds were at 210 degrees at 3 kts.; favoring the runway. The reason I wanted Runway XY was the fact it was the longest runway (5005 ft. runway distance available) that will allow me to have more room to stop if I did a low-end approach. She later informed me shortly that the winds were calm. This allowed me to approach to Runway XZ (the opposite side of Runway XY) since I was coming from the west side of the airport.The hydraulic smell was getting stronger and the student was bothered by it. I decided immediately to take Runway XZ since we can get on the ground sooner. She cleared me to land on Runway XZ and acknowledged her transmission. I performed a low approach onto Runway XZ so that I can have enough runway landing distance I needed to make the landing without applying right brakes. We touched down; and I immediately retracted the flaps to help transfer the weight of the aircraft from its wings to its landing gear to stop the aircraft. I told the student to apply the brakes slightly to see if he has some brake authority; he did but slightly so. I also slowly pulled back on the control stick to help bring the elevators up to allow aerodynamic braking as the aircraft was slowly decelerating. We came to a stop at Taxiway XX intersection and the student applied his right brake but with more pressure than usual and I wasn't able to help him because I have no right brake control. We both determined that taxiing an aircraft from that taxiway [the] ramp was not practicable and decided to let ATC know that we needed towing assistance. We then shutdown the engine and waited for tow support to arrive to help tow our aircraft to ramp.