В нашей семье рецепты передаются от бабушки детям.

The preposition в meaning “in” requires the prepositional case to indicate location. The noun семья (family) changes to семье in that case. Its modifying adjective наша also follows the prepositional feminine declension pattern and becomes нашей. So:

• наша семья (nom.) → в нашей семье (prep.)

рецепты is in the nominative plural because it is the grammatical subject—the thing that “is being passed down.” In Russian, the subject of a clause normally stands in the nominative case.

передаются is the reflexive/passive form of передавать (“to pass on”). Adding -ся turns it into “are passed on,” so the focus is on the recipes themselves rather than on who does the passing. Without -ся, передают would be active voice: “(they) pass on.”

• The preposition от (“from”) requires the genitive case, so бабушка becomes бабушки.
• The dative case marks the recipient of the action, so дети becomes детям.
  Together they express “from grandma” → от бабушки, and “to the children” → детям.

Yes, in a true passive construction Russian can use the instrumental to indicate the agent:
• Рецепты передаются бабушкой детям.
This is grammatically correct but less idiomatic. Using от бабушки (genitive + preposition) is more common when talking about traditions “coming from” someone.