First of all, we don’t use honorific suffix “さん” when we refer to any member of our family in the talk with others. We don’t say 私のお父さん（お母さん、お爺さん、お婆さん、叔父さん、叔母さん、お兄さん、お姉さん）. We say 私の父（母、祖父、祖母、兄、姉、叔父、叔母）, though I witness some youngsters violating this rule, and calling their mother by ‘お母さん’ in their conversation with their friend(s) in the train and coffee shops from time to time. Maybe it’s passable in informal conversation among young people today.
With the expression – “私は二人のおにいさんがいる,” your friend is right.
“私は兄がいる” sounds somewhat awkward, and “私には兄がいる” sounds perfect.
I’m unable to give you a clear reason why. But possible reason would be when you say “私は…いる（ある）,” it presupposes “You are something,” not “You have something.” Whereas when you say “私には…いる（ある）,” of which literal translation is “To (for) me, there is XX,” it’s closer to saying “You have something.”
Though I’m not sure whether you can buy this rational or not, “私は二人のおにいさんがいる” is not recommendable whether it’s delivered during an informal or formal conversation. .