If a bride says she is inviting immediate family, including siblings and their children, is it proper etiquette for her to exclude her one brother's children?

No, but it is her wedding, who is paying for it ? If she and her groom are paying for the wedding, they choose who they want to come.

Of course it is not proper etiquett to exclude one if other similar relatons are invited, but if there is trouble between them, maybe something you don't know about even,

I agree with Fr Chuck.

She can invite ANYONE she wishes, but if she is inviting her other siblings children but not her brothers children, something might be going on there that you do not fully understand.

Nope.