When somebody and me do something, in Spanish we must say "somebody y yo":
CORRECTO: Juan y yo
INCORRECTO: Juan y *mí/ Juan *conmigo
Logically, we must use the 1st Person Plural:
CORRECTO: Juan y yo vamos a recoger
INCORRECTO: Juan y yo *vaa recoger
In order to say all of us, use entre nosotros or entre todos:
Papá y tú vais a hacer la compra, mamá y yo vamos a preparar la comida, y luego entre todos recogemos – Daddy and you are going to do the shopping, Mom and me are going to prepare the dinner, and then
all of use will clean up the house