I sat in front of my sister on the dolphin, succinctly expresses the action depicted in your illustration.
Without the picture to aid in understanding, you may want to add ...that we were riding, onto the end of the sentence. A listener probably would not assume you were riding a dolphin unless you made it clear.
To sit in the front of something requires that you be inside the thing you are sitting in the front of. You can sit in the front of the train (meaning a train car at the beginning of the line of train cars or the first row of a particular train car) and you can sit in the front of the class[room] (meaning you are sitting in the front row of a classroom). You cannot, however, sit in the front of a dolphin unless a Dolphin is a type of boat.