How to handle my son who wants to play at neighbors house but i don't want him to?

I am a 36 year old mother of a wonderful 10 yr old boy. We have lived in a nice quiet town in illinois for 3 years. Well, it WOULD be a quiet setting if it weren't for our neighbors across the street. The woman who lives there is about 34 yrs old, married, and has a sweet, quiet little 8 yr old son. That poor kid can't do anything without his mother screaming obscenities at the top of her lungs at him. I mean it is REALLY horrendous. As much as I hate hearing it, I always mute the tv when this is going on (every day, every 15 minutes) to listen for any signs of physical abuse. I am not a nosy neighbor by any means. The yelling is so loud that we can hear every word coming from her house while we are in our house. There is a little girl who lives down the street who comes over to play with him after school. This does not stop his mother from her awful tirades. Im pretty sure she doesn't drink, she is just a verbally abusive parent. Well, yesterday, my son asked me if he could go over to his house to play. I was shocked when he asked that because he also has to listen to the noise coming from their house and has always said that he would NEVER want to play over there. My son doesn't even want to play in OUR yard when she is screaming at her son because he said it makes him feel bad. There are no kids in my sons class who live within walking distance of us. I can tell he is really wanting another child to play with after school, but not in a million years would I have expected he'd resort to wanting to go to the neighbors house. This makes me feel bad because her son is a nice little boy. He's very quiet but that's not surprising considering he gets verbally attacked every time he opens his mouth. And I know I could invite the little boy to our house but honestly, I don't want to have to deal with his mother AT ALL. He played at our house one time last summer and she started screaming at him from across the street to come home and "clean his ******* room or he was gonna get his ******* *** kicked". Pardon my language but that is exactly what she said and that's how she talks to him all the time.I do not want my son around that. Not even once. We provide our son a happy, loving home where he feels safe and loved. Im kind of struggling with how Im going to tell him he can't play with the neighbor boy without him feeling like im keeping him from having a playmate. I have no problem driving to a friends house with him to see if they want to play but basically he sees this little boy outside every day and just wants to get together with him. Im afraid that if they played together she may end up yelling at my son and I would have to take care of that real quick. Then there would be that annoying awkwardness every time our families see each other. It's amazing that it doesn't seem to bother her at all acting this way outside for the entire street to hear. I feel like this is going to turn into an every day battle with my son. I hate denying him a playmate but I absolutely DO NOT want him around this child's mom. Around the house my husband and I refer to her as "the beast" because that's really the only way to describe her. Am I over-reacting? Is is wrong for me to deny my son to have a buddy who lives across the street and is so easily accessible to play with? My gut says Im right to keep them separated but I always welcome input from others. Thanks!