This is very sad.
I don't spank my girls at all. Making a noise is enough to scare them. I had a Beagle that would pee and poo when he was scared because he was abused. However, he did settle down after he got used to us. I am concerned that fear is the main reason your Luke may be using the bathroom in the house.
In my opinion, the best option may be to rehome him. At least he would not be spanked.
Also, I have to say this: If you don't want accidents in the house don't get an inside dog. Maybe you could nicely remind your mother of this.
Maybe you should have your dad call animal control. It may be best to get Luke out of this situation.
I am so sorry you are having to deal with this at your age. Hugs and prayers to you and your furbabies.