Plurals with Clarification

It would be best to say, "My brother Brian's car..." No commas needed.

Remember that the rule that the apostrophe gums up here is that if you have one brother, you use commas; if you have more than one brother, and you are referring to only one, you do not use commas.

For instance, my brother Michael is married. His wife's brother, Jose, is single.

The 'my brother' part is an appositive, a description set apart from the sentence in commas. I would have to say the correct form would be

Bryan's, my brother, car...

Could be wrong here, but I would probably just reword the sentence for clarity as Rom does.

"Bryan's, my brother's, car" refers to the car belonging to Bryan, your brother.

"Bryan, my brother's, car" refers to your brother's car which he has named Bryan.

Hey, I had a high school friend who owned an orange Datsun that he'd named Julius. Weird guy.

But, I would also agree that it's best to say, "My brother Bryan's car..."

My vote is for "Or can you just not say that?"

Grammatically, you must be able to pretend that the nonrestrictive clause is not there, which eliminates the first option right away, because it becomes "Bryan car".

If you say "Bryan's, my brother, car," "my brother" is an attempt to explain what "Bryan's" is, which doesn't make sense.

The only one that seems like it might be legal to me is "Bryan's, my brother's, car," but that's just plain awkward. You might get away with something like "Bryan's--that is to say, my brother's--car," but even that's a little odd.

If language were more like computer programming or mathematics:

(Bryan (my brother) )'s car