We understand your concern for your family members' animals and their well-being. In all things, we should come before God in the name of Jesus, 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."
First, we would like to address the mention of only one vague reference to God. We are approaching God in the name of Jesus Christ. It is only by His name that we can be saved and approach God. We should not neglect this important fact. It is further written in Acts 4:12 WEB: "There is salvation in none other, for neither is there any other name under heaven, that is given among men, by which we must be saved!"
First, we pray for the health and healing of these animals, as God cares for all His creatures. Psalm 36:6 WEB reminds us that "Your righteousness is like the mountains of God. Your judgments are like a great deep. Yahweh, you preserve man and animal."
Let us pray together.
Dear Heavenly Father,
We come before You in the name of Jesus, lifting up the animals belonging to our dear one's family members. We pray for Your healing touch upon them, that You would restore their health and strength. Guide the veterinarians, giving them wisdom and discernment to accurately diagnose and treat these animals. We pray for the family members caring for these animals, asking for Your peace and guidance during this time. We also ask that You would provide for their needs financially, easing the burden of medical costs.
We pray for the financial needs of the family. It is written in Matthew 6:31-34: "Therefore don't be anxious, saying, 'What will we eat?', 'What will we drink?' or, 'With what will we be clothed?' For the Gentiles seek after all these things; for your heavenly Father knows that you have need of all these things. But seek first God's Kingdom, and his righteousness; and all these things will be given to you as well. Therefore don't be anxious for tomorrow, for tomorrow will be anxious for itself. Each day's own evil is sufficient."
Father, we pray for the animals. In Psalm 50:10-11, You, God, own the cattle on a thousand hills and the beasts of the field are yours. We are merely your stewards of these animals. We ask for healing and a long satisfying life for them.
We ask that You would put people in their path who would share the good news of Jesus Christ with them, that they may come to know Him as their Lord and Savior.
In Jesus' name, we pray. Amen.
In regards to the finances, while we should pray for financial burdens we also want to keep in mind that giving our tithes and offerings are important to receive God's financial blessings. It is written in Malachi 3:8-10: "Will a man rob God? Yet you rob me. But you say, 'How have we robbed you?' In tithes and offerings. You are cursed with a curse; for you rob me, even this whole nation. Bring the whole tithe into the storehouse, that there may be food in my house, and test me now in this," says Yahweh of Armies, "if I will not open you the windows of heaven, and pour you out a blessing, that there shall not be room enough for."
In regards to the animals, we want to take a look at the bigger picture. Humans and animals alike belong to God. God cares about the animals and has made us stewards over them.
Lastly, we want to encourage sharing the Gospel with others. We encourage everyone to share the good news of Jesus Christ with others. We are reminded in Romans 10:13-14: "For, 'Whoever will call on the name of the Lord will be saved.' How then will they call on him in whom they have not believed? How will they believe in him whom they have not heard? How will they hear without a preacher?"
Prayer Focus: God, Thank You for loving me. God, I ask You in Jesus’ name please bless me with everything that I stand in need of and everything You want me to have. 
