This is a very opinionated question so please give me your detailed opinion and don't forget about the last line in this question. I for one believe that her family did have the right to publish her poems as long as she didn't tell them not to because her family knew how great her work was. I believe that Dickinson didn't publish them herself because she was afraid of what the public's opinion would be of those poems.
Selfishly I am incredibly glad that her family published her poems, and to be honest, depending on what you believe about what happens to you after death, I don't really think Emily Dickinson is too bothered now! What we have gained in spite of contravening the will of Emily Dickinson is far more than what we would have lost if her wishes had been carried out.
Emily Dickinson's family had good intent, I'm sure; they had no way of knowing then that her work would be so well received, so their motivation was probably not money. Pure motives go a long way toward forgiveness, if any is required. I think of a similar situation with Anne Bradstreet in Colonial times, when her family published a volume of her work of which she was unaware. The book, I believe, ended up being copied and sold in England without any benefit to her (for there were no copyright protections then, of course), but it has made her one of the only female voices represented from that time period in America.
Because we are such a litigious society today, we concern ourselves with the issue you mention. Perhaps the family of Emily Dickinson did not have a legal right to publish her poems, but perhaps, also, they saw the worth of them and felt that millions could share their beauty. Indeed, we are all the richer for having shared in her metaphors on life.
There are some really contentious issues here surrounding intellectual property: most of which would not have been a feature of the time immediately following Dickinson's death.
It has been said many times that Dickinson lived through her poetry: that as a recluse her unique work was created from intense sensitivity, empathy and of course imagination. It is only fitting that as she lived through her poetry, so her poetry should be used to recognise and appreciate her life and the gift of poetry she left behind.
Although I am very glad, obviously, that her works were published, I do have concerns about family members publishing them after her death, although no harm has come of it. Some authors are intensely private (Dickinson being one of them) and did not know that their work would become SO huge after their deaths and I believe that some authors would be rather distraught that some of their work was published. With that being said, however, the families, I'm sure, only wanted to share with the world the massive talent of these authors that were in their families.
After her death the poems no longer belong to her. She has left them behind for her family to deal with as they see fit. Personally, I am thrilled that they did publish them as we would not have her clever views on life otherwise. When a person dies, does he/she care what happens to what he/she leaves behind? I think not. Of course she was concerned with public ridicule...she wrote once that she hoped the world would be kind. Her fear of rejection was unfounded since her poetry is great. Anything she leaves behind after death legally passes ownership--they no longer belong to her, so the family does have the right to do what they wish with those poems.
The question posed is purely a legal matter relating to copyrights and inheritance laws. The copyrights of all works belonging to any work belongs to the author. This copyright is like any other property in the sense that the copyright holder has the right to any royalties earned on that work. Unless the author assigns the copyright to someone else, it remains the property of the author till his or her death, and after death passes on to the heirs. Heirs inhering the copyrights then have the freedom to use this property inherited as they consider appropriate.