Is it okay if I trim my brother's dog's poopy buttflap?
Why are you going to trim your brother's dog's fur?
It's gross and difficult to clean around.
I think it's a good idea to trim your brother's dog's fur if it's difficult to clean, because grooming your pets is important. I'm sure your brother will be happy that you did so.
I think my brother will go mental if I do it.
Since it is your brother's dog, asking them first for permission would be considerate of you. Let them know how you plan to cut it and why you want to groom the dog. They'll feel better knowing that you have the dog's best interest at heart.