Your thanksgiving to God is beautiful and right, and it is good to join you in praying for your mother.
Scripture places great weight on honoring father and mother, and that honor was never meant to be only words. It meant to care for them, to provide for them and to look after them when they grow older, since they cared for us when we were young. Your prayer for your mother's health and long life is part of that honor, and God sees it.
We also see how much Jesus cares about sickness. He healed a leper on the road, He healed the servant of a Roman officer at a distance, and He healed Peter's wife's mother when she lay sick with a fever. In the evening many others were brought to Him who were sick and troubled, and He healed them. Matthew connects this to what Isaiah wrote, that He Himself bore our infirmities and carried our sicknesses. That shows His power over the physical body and also over the spiritual realm, and that He is still able to heal today.
Faith in Him matters. Sometimes people needed a point of contact to release their faith, like those who reached to touch the edge of His garment, believing that in that moment they would receive His help. Another mother came to Jesus desperate for her daughter who was severely afflicted, and she would not leave until she received an answer, and her faith triumphed. You can come to Jesus in the same persistent way for your mother, bringing her to Him again and again and not going away until you have placed her fully in His hands.
The letter of John to Gaius contains the wish that he would prosper and be in health even as his soul prospers. That was a loving greeting, not a formal promise that every believer will always be well, but it does show something true. God is interested in your health, and there is a real connection between the well being of the soul and the well being of the body. Attitudes, peace, and trust in God affect us deeply, and God also cares about the practical stewardship of our bodies in what we eat and how we live.
You do not need any other intercessor to reach Him. When people said His mother and brothers were waiting outside, Jesus pointed to those who do the will of God and said they are His family. That teaches us we have direct access to Him through His name alone.
So we pray with you now. Father, in the name of Jesus we thank You for the healing You have already given and for Your mercy. We lift up this dear mother to You and ask for Your hand upon her. Grant her health, strength, and length of days according to Your will. Keep her body and keep her soul, draw her closer to Jesus, and give her peace. Help those who love her to honor her well by caring for her faithfully each day. We trust Your compassion and Your power to bear our infirmities, and we ask this in the name of Jesus, Amen.