Well I think this is going to be very hard on your hens. This is going to continually to cause a lot of tension in the flock, and I rather doubt that the fight is over if the hens are still choosing the old rooster.
Not all birds will work in your flock, if you are raising a lot more hens, how old are they now? If they are chicks, it will be months before they are ready for a rooster. And months is a long time for the 4 hens to have to deal with 2 roosters.
To have two strange to each other roosters, work in a flock, you would need IMO, a flock of 25-30 laying hens and the space for those birds. Hens that are currently laying before being introduced into the flock. Roosters really do not get the concept of sharing hens. And they are going to be pretty much, constantly fighting, and constantly trying to dominate the hens. I would expect the 4 hens to be worn out with all of that, they will start to hide and eat less.
Chickens won't just be nice and get along. Perhaps I am misreading they whole set up, but I am a bit worried about your coop size, and the area of your run? Often times if people only have 5 birds, the set up is for a smaller flock.
It would be helpful to know the ages of the pullets, and the number of pullets. The size of the coop and run to give more positive information. But with the information you are presenting, I would strongly suggest giving the new rooster back. Even if that means that who ever had him, will cull him. Don't ever take birds you feel sorry for, they just tend to ruin your flock dynamics.
IMO - you have set yourself up for ongoing cock fighting, and highly harassed hens. There may be a bird or two who die over the fighting, and I would expect the egg laying to go down. Perhaps I have misjudged the situation.
Mrs K