The pain you are describing is very real and it is understandable why you feel hurt and alone. To be invited with a promise of help and care, especially while facing a difficult health diagnosis, and then after only a short time to be treated coldly and told to leave, is a deep wound. It is even more painful when you see the same unkindness shown to others in the household, and you are left by yourself much of the day and night without warmth or support.
Scripture places a strong emphasis on family loyalty and care. It teaches that those in a family have a responsibility to look after one another, and that to refuse to care for your own household is a serious failure of love and duty. When that duty is set aside, the hurt runs deep because family is meant to be a place of refuge. Even Jesus knew what it was to be rejected and misunderstood by those closest to Him, and He understands the sting of being dishonored in your own family. At the same time, the Bible speaks of another family, the family of God, where He places people together in love and where the bonds of faith can bring comfort when blood relationships are strained or broken. Your longing to see kindness and faithfulness restored in your sister's home is right, and the best place to take that longing is to prayer.
The Bible also presents God as the one who steps in as a redeemer when family members cannot or will not do what they should. In the story of Ruth, the kinsman redeemer was the one who willingly took responsibility to protect and provide for someone who had no other help, to secure her future and her home. That picture points to what God Himself does for His people. He sees your arthritis and the weariness it brings, He sees the loneliness, He sees the need for a safe and affordable place to live, and He does not turn away. He promised Jacob that when he returned to the place God was leading him, God would be with him, and that promise is still true. God is with you in this unsettled place, and He is able to provide what you need, whether through opening the right door for housing, through help with your disability claim, or through His own daily strength and peace when conflict surrounds you.
God's desire for marriage is that it be a lifelong covenant marked by kindness, respect and faithfulness, not by coldness or a wish to live as if single. It is not good when a husband or wife is treated with meanness, and it is right to grieve that.
I am praying for you, that God will bring healing and comfort for your body, that He will give wisdom and favor in the process of your disability claim, and that He will provide a safe, affordable home where you can have peace and privacy, the kind of single home with a fenced yard you have asked for. I am praying that He will guard your heart from bitterness while you wait, give you peace that passes understanding, and surround you with people who will show you the care of His family. I am also praying for your sister, her husband and her daughter, that God would soften hearts, bring repentance where it is needed, and restore kindness and honor within that household.
May the Lord who is your redeemer and provider keep you, give you strength for each day, and lead you to the place of rest He has for you.