no way you should be cleaning up after him, let alone being responsible for his room. In my house growing up, I was responsible only for my own room, not others, along with the shared chores of kitchen and such.

If someone is so drunk that they vomit or make a mess of the bathroom it should be on them to clean it up otherwise it's simply enabling them more to continue the bad behavior. If your mom wants to enable him, let her do so but she should not include you in this behavior of keeping him in this pattern of drunk behavior.