It would be "Diana prefiere que nosotros tragamos la comida para las vacaciones" because you have to conjugate the verb "tragar" for Nosotros, so you would replace the "-AR" ending with "Amos".
Answer:
more context needed please
No sabra decirte la verdad puedes especificarlo un poco
The error in the sentence is somos. El pollo is singular so somos must be singular.
Correct:
El pollo es delicioso.
