Can step parent file a petition for joinder?

A joinder brings legally interested parties into the case. A stepparent is not such a party.

A motion for joinder is usually brought to bring a "necessary and indispensable" party into an action; and, in Family Law cases to bring in a party who claims or controls an interest in any matter subject to disposition in the action (California Rules of Court, Rule 5.24) Subsection (c)(1) includes any person who has or claims physical custody or control of a minor children subject to the action. However, simply being an interested party is insufficient to be joined to an action. You really need the advice of an experienced family law attorney who can elicit the facts necessary to give you advice on this issue.