If my child's father has been convicted of domestic abuse during our supervised visits and never took court ordered drug tests will Indiana courts still allow visitation to him?

Its possible. Who was doing the supervising during the visits with the child?

His parents were supervising the visits. He didn't show on several visits and has never paid support. He abused me in the past though I have no charges pressed against him. I only have no contact orders and a harassment police report. He has now been arrested 4 times in the last year for beating his new wife. I'm scared to allow my son to supervised visits at his parents due to abuse to me that has occurred there along with his new wife. His parents hide his problem and his father is preacher. I'm scared for my child and also this new wife's children.

Then change the place here the visits are supervised. Most States and jurisdictions have visitation centers. You could ask for that in court.

I know here in Atlanta there are professional supervision centers, where a child can be left off for the visits.

But the court order for visits are valid unless you go back to get it changed