Hi Cinnamon,
It may be confusing to play while the recording is going -- (which includes the piano part)..
But i would study the whole score, and also listen to the recording while following the score, to become familiar with the other parts.. Of course, the interpretation of the piece in the recording - shouldn't be too weighted. This is just for the purpose of becoming familiar.. From an interpretative stand point, i think it best to start from the indications of the score.. And your coach may have a completely different idea of interpretation than your recordings..
Also, the more you are comfortable with the piano score, the easier it will be to listen carefully to the others in the ensemble… This listening is a key part of the fun of playing with others..
You are going to have a great time, I am certain.
ps.. which trios are you considering? I love the Mendelssohn.. (usually though it is Mozart and Beethoven that get much of the attention - when being introduced to chamber playing..