Is there Biblical evidence to show how the Father and Holy Ghost felt when Jesus hung on that cross?
There is no direct Biblical evidence, but by the fact that God caused the sun to go down for 3 hours in the middle of the day along with triggering an earthquake, and splitting the Temple veil indicates it was an emotional time. Amos 8:9-10 gives some indication of the extent of His emotion.
“In that day,” declares the Sovereign LORD, “I will make the sun go down at noon and darken the earth in broad daylight. I will turn your religious feasts into mourning and all your singing into weeping. I will make all of you wear sackcloth and shave your heads. I will make that time like mourning for an only son and the end of it like a bitter day.”
According to some who understand the Aramaic language, when Jesus said, “My God, My God, why have you forsaken me?” (Matt. 27:46) He was speaking to both the Father and the Holy Spirit, overwhelmed by the intensity of the anguish He felt upon being separated from them. You and I don’t know what it’s like to be completely one with God, but He had never known separation. Perhaps they felt the same.