Crazymama, you said, "Many times when he yells at difficult child I will tell him he does not need to yell, there is no need to be mean. He looks at me blankly, ignores that I have said anything, and does his own thing."
I'm thinking you may be right about him just not understanding what you mean. How about you model it for him? Keep it light and not too heavy, but if you said to cousin, "In this house, we have a rule. We speak to each other with respect. Here is how you just spoke to difficult child - [give example]. Now this is how you SHOULD have said it - [give example again]. If you show respect to people then they are more likely to help you and show respect to you."
If you need to, make him repeat it nicely after you, then praise him if he gets it right. Make it clear - your rules in your house.
It's amazing how even a difficult child can 'get it' with different rules.
Example - my eldest sister's kids. With hindsight we know just how VERY difficult child the three middle kids were especially. My sister lived next door. I often babysat them in her house and at our house.
In their house - they would run everywhere, jump on the furniture, spread toys and books everywhere, raid food from cupboards and fridge, run in and out without shutting the screen door... you get it. But next door at Grandma's house - the screen door MUST be shut (and it was harder to do, as well). Nobody permitted in the living room without permission. Nobody permitted in the bedrooms without permission. Toys and books - you get out what you are playing with and put the other things away before you go on with play. Want food - ask nicely, you will get what you want if it's not too close to dinner.
Even the youngest ones learned quickly.
I'm not saying my mother was a better disciplinarian - my sister was happy with how things were in her home, she had a house full of kids and they followed HER rules well. She was comfortable with boisterous behaviour and mess now and then. It's just that my mother wasn't, but still allowed the kids some space and mess. The kids learned the different standards and rules and modified their behaviour according to which house they were in.
If Grandma was babysitting the kids in their own home - they would jump on SOME of the furniture and still leave the screen door open sometimes.
It's OK to make changes to your own rules, too, but you need to communicate it well and give some leeway as the new rules are being learned.
Another example: I was raised fairly strictly, but with clear rules. It was a Christian Protestant household, very pragmatic. My best friend was Roman Catholic but the house rules were much looser.
I stayed overnight a couple of times and was mortified to discover I was expected to say my evening prayers. In our church children were NEVER expected to pray aloud while improvising - the only praying aloud we ever did was Lord's Prayer, with everyone else. So when my friend's grandma told me to say my prayers and get into bed, I didn't know what to do. I asked for privacy and managed to improvise something with grandma outside in the hall (she was a lovely lady, very kind). And I'm sure when my friend stayed overnight at our house, she felt just as uncomfortable (and probably felt we were heathens for not praying aloud at bedtime!). With time it was no big deal. We talked about it, we worked out the differences and similarities and got on well.
I would be congratulating difficult child on his patience, tolerance and understanding. He is a credit to you. And maybe he now has more sympathy for easy child's frustration with him?
Marg