Can the first wife object to her husband's polygyny application?

Yes — the wife is entitled to raise an objection with reasons and evidence, but the final decision lies with the judge. The most effective objection is one that concerns the legal conditions: for example, the husband cannot afford to provide, has already neglected maintenance, has acted unjustly, or the marriage will harm the wife and children. An objection without evidence relating to the conditions is usually not enough, because polygyny itself is permissible in the Shariah — but your concerns and feelings are still valid and worth stating to the court. Prepare documents such as financial statements and maintenance records. Consider the services of a Syariah lawyer or the legal aid bureau. See polygyny in Malaysia.