We understand your situation, and we empathize with the weariness and strain you're experiencing. Above all, we want to remind you that God is sovereign over every aspect of our lives, including immigration processes. As it is written in Romans 13:1, "Let every soul be in subjection to the higher authorities, for there is no authority except from God, and those who exist are ordained by God."
However, we want to address that the ultimate goal of our prayers should be for God's will to be done, not merely for our own desires. We pray that if it is God's will for you to be with your family and obtain this green card, that His will be done. But we also trust that God has a plan even if the green card is not approved as quickly as you hope.
We also note that your request does not mention the name of Jesus Christ. It is through Jesus that we have access to the Father (John 14:6, "Jesus said to him, 'I am the way, the truth, and the life. No one comes to the Father except through me.'"). So, we will be praying in His name.
Let us pray together:
"Dear Heavenly Father, we come before You in the name of Jesus Christ, lifting up our brother/sister who is anxious about their green card approval. We ask, Lord, that if it is Your will for them to be reunited with their family quickly, that You would move mountains and expedite this process. But above all, Lord, we ask for Your will to be done and for our brother/sister to have peace and strength in this time of waiting. We pray that they would trust in You, for You are their strength and their shield (Psalm 28:7). In Jesus' name, we pray. Amen."
In the meantime, we encourage you to meditate on Isaiah 40:31, "But those who wait for Yahweh will renew their strength. They will mount up with wings like eagles. They will run, and not be weary. They will walk, and not faint." Trust in the Lord, and He will give you the strength to endure this time of waiting.
Prayer Focus: God, Thank You for loving me. Thank You for loving me, Jesus. God, I ask You in Jesus’ name bless me with everything that I stand in need of and everything You want me to have. Bless me to know You in truth, fall in love with You with all my heart, soul, mind, and strength and never fall out of love with You. Bless me to have an ever growing closer stronger, more intimate relationship with You. Bless me with the love, desire, strength, and the spirit of obedience to always delight myself in You, seek first Your kingdom, and Your righteousness. Help and strengthen me God to always respect and obey You. Bless me to trust You with all my heart, acknowledge You in all my ways, and lean not to my own understanding. 
