Oh dear, everyone's children do these things, but it's so hard when they do. My day is going along a similar path to yours, judging by your question, so I am empathetic to you. It's so annoying because we expect to see fraternité and, when it doesn't happen, we're saddened and disappointed and annoyed.
So, how to deal with it. There are a few steps to managing this gently. The first step is to understand that this behaviour is an expression of an unmet need. Neither of the boys are going to be able to express what this unmet need is in clear English, even if they are asked to express what's going on, so we need to work with them to meet their needs and hold on to reasonable limits.
Let's start with the elder. When he goes to mimick his younger sibling, we need to stop him and remind him about his behaviour. Stop him and say, "mimicking your brother is disrespectful, I won't let you do it". Now, he may cry, which is good. As I've said in other responses, crying allows him to release all the feelings he's been hanging on to and that are frankly behind the behaviour. He may even need a time-in, which gives him a chance to rage and rant and get the ugly feelings out so he feels better and is more amenable to compromise and helpfulness.
Similarly, when your younger purposefully does stuff to annoy his older brother, same same.
As for the cousins, that might require a quiet word in their parents' ears. If they can be brought on board, as a kind of benevolent leader in these febrile situations, all the better.
Believe me, I know it's hard. I'm having a tough day today as I write this with children refusing to do as they've been asked. We both need to remember that children are looking out for us to be consistent and to hold a (reasonable) limit.
We need to remember we can't force them to do the right thing, we can threaten and cajole but, ultimately, we want them to make the right decisions because they're right, not because we are holding their hands to the fire on a limit. If our limits are reasonable, and I believe mine today are and I believe yours are too, then be patient and hold the line. They will come around eventually, and they'll be upset and cry when the limit is held but they will see our resolve and be grateful they know where the limit is.
This style of parenting is no quick fix, and we need to support and reassure each other that we are on the right path to having children who do the right thing because it's right, not because they fear punishment or expect a reward.