Sounds like the two aren't going to get along...ever, unfortunately and it is just going to get worse as far as the severity of dangerous situations go. They both might be competing for dominance and neither wants to back down which means no pack formation will ever be in place and it won't work no matter what you do. I don't know much about the beagle breed but he could be simply stubborn and not want to back down in trying to be the "pack leader".
I have males together in my house, one dobe but male poms, but thankfully no one fights, not even play fight (well, he play fights with my female pom constantly but he's gentle with her and she gives it right back lol) thankfully it is working out great, however we don't take our eyes off them no matter how great it is just to be safe. But with your situation, just as doberlover said, this is an example of how male/male aggression can be. For some people, two males works for others it doesn't. Please be weary that one of them could end up getting hurt due to the situation, and most likely it's going to be your brothers beagle.
I have males together in my house, one dobe but male poms, but thankfully no one fights, not even play fight (well, he play fights with my female pom constantly but he's gentle with her and she gives it right back lol) thankfully it is working out great, however we don't take our eyes off them no matter how great it is just to be safe. But with your situation, just as doberlover said, this is an example of how male/male aggression can be. For some people, two males works for others it doesn't. Please be weary that one of them could end up getting hurt due to the situation, and most likely it's going to be your brothers beagle.
