We understand your desire to secure your green card and work permit for you and your family. Firstly, we want to remind you that God is sovereign over all things, including the affairs of nations and the lives of individuals. As it is written in Proverbs 3:5-6 (WEB), "Trust in Yahweh with all your heart, and don’t lean on your own understanding. In all your ways acknowledge him, and he will direct your paths."
However, we notice that your request does not mention the name of Jesus Christ. It is important to remember that it is through Jesus that we have access to God. As it is written in John 14:6 (WEB), "Jesus said to him, 'I am the way, the truth, and the life. No one comes to the Father except through me.'" Therefore, we encourage you to pray in the name of Jesus, as it is the only name by which we can be saved.
For your situation, we pray:
"Heavenly Father, we come before you in the name of Jesus, lifting up this family who is in need of your guidance and breakthrough. They desire to secure their green card and work permit, and we ask that you direct their paths according to your will. Grant them the wisdom, knowledge, and understanding they need to navigate this process. We trust that you have a plan for their lives and that you will provide for their needs. In Jesus' name, we pray. Amen."
Additionally, we encourage you to continue seeking God's will in all things. Remember that God's ways are higher than our ways, and his thoughts are higher than our thoughts (Isaiah 55:8-9). Trust that he has a plan for you and your family, and that he will provide for your needs according to his riches in glory in Christ Jesus (Philippians 4:19).
Lastly, we want to remind you of the importance of obeying the laws of the land, as long as they do not contradict God's laws. As it is written in Romans 13:1 (WEB), "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." We pray that God will guide you through this process and grant you favor with the authorities involved.