Your desire that the Lord be glorified through this difficult season is itself pleasing to Him, and I thank you for sharing your heart so honestly.
The God to whom you are praying is full of compassion and gracious, slow to anger and abundant in mercy and truth. That is His character in both the Old and New Testaments. He is also a God of righteous judgment, yet His heart delights to show mercy, and His mercy endures forever. The Scriptures repeat that truth over and over so it will be planted deep in us, so we will never doubt that He is ready to forgive and to help when we call on Him, even when our trouble has come through our own failures. When we cry to Him in distress, He hears and He saves, not because we have earned it but because His mercy is without limit and as high as the heavens.
That is why you can come to Him with confidence in this situation. Mercy is not something we deserve or can demand. As He said to Moses, I will have mercy on whom I will have mercy and I will have compassion on whom I will have compassion. It is not by our resolve or our effort, but by God who shows mercy. He is sovereign, and yet He was looking for a reason to show mercy to His people even when in justice He could have judged them. Knowing that He is plenteous in mercy gives you ground to pray as the psalmist did, turn to me and have mercy on me, give Your strength to Your servant.
I am praying with you on that basis. I am asking the Lord to show His mercy toward you in the eyes of the managers of the home where you are staying, and if it is His will, to soften their hearts toward you. Whether He does that through them staying His hand or through another provision, I pray He will make His will clear and give you peace. I am also praying that He will be your strength and your portion right now. He is the strength of your life, your light and your salvation, so you need not be afraid, for He keeps those who are His. He has promised to give strength to His people and to bless His people with peace, and to cause those who trust Him to go from strength to strength as they appear before Him. His goodness and mercy will follow you all the days of your life, through this pilgrim journey, and at the end of the path He will bring you to dwell with Him.
Remember too that Jesus was forsaken by God for a moment on the cross, crying My God, My God, why have You forsaken Me, so that you would never have to be forsaken by God eternally. You are not abandoned now. The true and living God is not only the One we want in a moment of crisis, He is the One who is wonderful to live with every day. Walk with Him daily, seek Him with a heart fully turned toward Him, call on Him through faith in Jesus Christ by whom we are made righteous before God.
May the Lord turn to you and be gracious to you, give you His strength for each step, guide you and keep you, and use your life for His purposes. May He be glorified in how you trust Him through this, and may you know His peace that comes from knowing His mercy endures forever.