M.D.
I strongly disagree that she shouldn't be allowed to have privacy in her own room. She thinks of her room as her own personal little place where she can do what she wants and her brother is intruding. If not at age 3, then when? I believe children should expect to be treated with respect (and that is what this is, a matter of respecting her right to privacy, unless of course its a safety issue) at any age, by her brother, by her parents and by anyone else.
For practical purposes, explain to her brother that if he wants to play with his sister, it must be in neutral territory. Make the livingroom the designated play zone.