I am a retired police officer who has investigated sex offenses including those involving children. Your description immediately caused me to wonder if this boy has been or is being molested. Looking at and showing private parts is common but this sounds like there is the possibility that it is more than that. In addition to the boys behavior the father is defensive.
I recommend that you call your local police jurisdiction information line and tell them you'd like to talk with someone about child molestation. When you reach that department tell them what you've told us. They will ask questions and perhaps want to talk with your daughter.
Definitely do not let your daughter play with this boy and have contact with the father. Do not let her play outside by herself.
When my grandchildren were that age their mother and I both agreed to not let them play outside by themselves and it was sometimes an inconvenient but we were able to do that. They live in an apartment complex and I am aware that even tho you want to trust others you cannot until you actually know them well. Even if everyone in the complex was trustworthy you do not know who will come by.
My granddaughter is now nearly 10 and her mother still will not let her play outside without an adult she trusts also outside. I might be a bit more relaxed but I still think it's best to err on the side of safety.
It must be disappointing to move into a house in a quiet area and have to deal with this possibility. I sometimes feel so sad that our world today is so different from the one in which I grew up. When I was a child we could roam the neighborhood. All the families knew each other and watched out for each other's kids.
I do want to emphasize that this may not be a case of molestation. It could just be that this father is allowing his son to watch inappropriate TV programs, movies, even himself and a girl friend. Even if that is the case you do not want your daughter to be exposed to it.
And, your call, may help the boy by bringing the father's inappropriate parenting to official attention.
You mention avoiding the son and father. Is there something about the father that causes you to fear him? I've found it's usually best to be up front about things. Unless you have a gut feeling that you can relate to something he's said or did that causes your fear, tell the son that your daughter cannot play with him because he's too old. Tell the father the same thing. It is reasonable that an 8 you and a 4 yo not play together. You don't have to tell them anything else.
If you do not have a fence, I also recommend that you build one with a gate that can be locked. I wouldn't want my 4 yo playing outside in an unfenced yard. Both of my grandchildren wondered at that age and still do. They're interested in knowing about everything. Even when I was a kid and we felt safe from predators my parents built a fence around our back yard.
It really is best to be safe than sorry.
Later, I want to add that calling the police and/or Child Services does not open one up for a law suit of any kind. The purpose of your call is to gain information on how to protect your child. It is not even to report the other parent although in this case the police and/or Child Services will investigate if in their opinion there is a need for more information. Calling is not make an accusation. It is asking a question.
I also agree that this can be normal behavior for an 8 yo. That is why it's not appropriate for a 4 yo to play with some 8 yos. I'm not saying it's always inappropriate.
I am saying that I'm concerned because of the totality of the information. I have received similar information and found that even tho the situation wasn't a good one there was nothing that I could legally do except offer the parent some assistance. Some parent's accepted the assistance. Some didn't.
If you do not want the father of the other boy to know that you are the one that called you can ask to be a confidential informant. It is likely that he will guess that you are the one that called and the authorities will help you deal with the fall out if there is any.
I definitely believe that you should not get the two families together. You do not know the other father well enough to know his reaction. The likelihood of this being traumatic for you and your daughter is high. He's already shown that obscenity is a part of his language.
I do suggest that if he wants, to your husband could talk with the father about what has happened. But again, from what you've said about his defensiveness I believe that this will not help. In many circumstances I do believe that talking with a neighbor first is a good way to be a good neighbor. But, it sounds to me, that this man is not able to be a good neighbor. He shows this by being critical of other children in an angry way.
If he does decide to talk with the other father he needs to be aware that whatever he says needs to be the truth and said calmly. He doesn't have to talk about everything but what he does say should be accurate. What brings this to mind is the suggestion that your daughter will not be allowed to play with any older child. This is setting you up for difficulty if you do have an older child over to play and that is a possibility.
I am always in favor of protecting one's self and especially one's children. this doesn't mean that you have to talk with the neighbor if doing so will cause you to be verbally abused. We say that neighbors should talk with each other. Unfortunately that is not always possible.
Getting as much info as possible and thus being able to make an informed decision is talked about often now. Calling the police/and/or social services is a part of the process of making an informed decision about one of the most important parts of your life; that of the life of your child. Calling is a positive move and not a negative one as is intimated by some of these posts. You make the call to learn and inform and not out of anger and spite. There is a huge difference that professional people are well aware of and most often able to discern.
As other moms have suggested, if you haven't already begun to do so now is the time to have the "good touch, bad touch" conversation. There are some good books geared to a child her age that also have a page to help parents with this conversation. You can find some at the public library. A general rule to give her is that the area of her body that would be covered by a swimming suit is private. Then you can tell her who in her life is OK to see that area.
I liked Faye's post with a list of rules. Modify those to fit your family. Having such a list will make it easier for kids to know what is appropriate and what is not in your family. I raised a foster/adoptive daughter and relied often on the phrase "in our family." This is a positive way to teach values without judging others' values.