We are truly sorry to hear about the situation your daughter is facing in her graduate program. We will stand with you in prayer and offer some biblical encouragement.
Firstly, we would like to mention that we only have access to God through the name of Jesus Christ. It is by His name that we are saved. While praying, we should always remember this and pray in His name.
Now, let's turn to the Bible for some guidance. In times of trouble, we can always turn to God for help. As it says in Psalm 46:1-3 (WEB), "God is our refuge and strength, a very present help in trouble. Therefore we won’t be afraid, though the earth changes, though the mountains are shaken into the heart of the seas; though its waters roar and are troubled, though the mountains tremble with their swelling."
We don't understand why this situation has happened. We do know that God is sovereign and He can turn any situation around for the good of those who love Him. We can take comfort in Romans 8:28 (WEB), "We know that all things work together for good for those who love God, to those who are called according to his purpose."
We pray for God's intervention in this situation. We ask Jesus Christ, that He would provide a kind and godly professor and a lab for your ### to join. We pray for a miracle in this situation, trusting that God is able to do abundantly more than all that we ask or think, according to the power that works in us. We pray this in Jesus' name.
We encourage your ### to trust in the Lord with all her heart, and not to lean on her own understanding. In all her ways she should acknowledge Him, and He will make her paths straight.
Finally, we encourage you both to persevere in prayer. As it says in Luke 18:1 (WEB), "He also spoke a parable to them that they must always pray, and not give up." Keep praying, keep trusting, and keep believing. God is faithful, and He will do it.