First, why do you want a rooster or both roosters? What are your goals relative to roosters? The only reason you need a rooster is that you want fertile eggs. Anything else is personal preference. There is nothing wrong with personal preferences, I think they are important. I generally recommend that you keep as few roosters as you can and still meet your goals. That's not because you are guaranteed problems with more roosters, just that more problems are likely. Your goals are going to be different from mine and it's your goals that should drive this decision.
Some people do keep multiple roosters with the flock successfully but some can't. The males may fight to the death or they may reach an accommodation in how they protect the flock. Often that means they each set up their own territory out of sight of the other and each keep their own harem. How much room they have is an important factor in behaviors. Some people do keep multiple roosters in much less space but the more room they have the more likely are to get along.
In Wyoming this time of the year it is possible that weather recently reduced the space available to them which may have triggered this behavior. But you don't really have roosters, you have cockerels. The are still maturing. What it sounds like to me is that your Wyandottte was slower to mature but he finally has and staged a palace revolt to take over. He is making sure that the Welsummer understands that. It's possible if you leave them alone that they will work it out in a day or two or it's possible it will be a fight to the death. Every time you interfere the process is pretty much going to start over.
Even if they work it out and get along for now it is always possible there will be skirmishes in the future. Usually these are minor but you never know when they can escalate into a fight to the death.
I don't know your goals or your set-up so I can't tel you what to do. I try to make these decisions for the benefit of the flock as a whole and not for the benefit of any individual bird.
