You will need a lawyer's help here, unfortunately. You have a right to have these photos removed, but it will require good knowledge of Internet-related law and probably matrimonial law, as well as judgment and experience in dealing with delicate situations such as this one.
If you are perceiving even some of these facts correctly, this sounds like a potentially explosive situation, with a lot of risk for you in a lot of different departments -- your career, possible criminal exposure, and potential interpersonal liability. You would be well advised to speak to an attorney with experience in employment law in your area as soon as possible.
Your question has a lot of important factual issues balled up in it. Who and what constitutes this "group"? Why is your employer implicated -- is it a group at work? What kind of office or shop do you work in? Are you a union member? Are you in management? Is the speaker in management and senior to you? Has your career been affected by these statements?
It appears that it makes sense for you to find a lawyer with experience both in employment law and defamation law to listen to the...
Yes, you do need proof -- proof that your competitors made disparaging statements of what appear to be fact; proof that they are in fact false statements; and proof that these statements have damages you or your company or could damage you in some concrete way.
Yes, you can.
If the work is original and you own the copyright, the fact that others, their heirs or their licensees may have claims against you -- as the other responding attorneys here have explained, as usual, very comprehensively -- would not bar you from still enforcing your copyright in the work. But if you ultimately were required to disgorge your profits from that movie, or worse, such copyright enforcement may be a Pyhrric victory for you!
Unfortunately, while there may be, technically, a way to get him to stop -- you may be able to bring a defamation suit against him if he is making factually false claims that are harming someone -- it's almost always a bad idea to do so. Few such claims succeed; it is expensive to bring them; and the publicity resulting from filing the lawsuit always ends up bringing more attention to the blog posts you don't want people to see than they ever would have gotten otherwise.
This is not legal...
As usual, Pamela Koslyn has done a great job answering. As you can tell from her answer, you are really going beyond the strict confines of copyright law into the realm of "art law," and considering what you seem to be contemplating, you need to sit down with a qualified lawyer who is experienced in that field and to get the advice you need specifically tailored to you.
Ultimately they do have to prove that the DVD's were counterfeit, yes. There are ways to do that without having the actual hard copy of the DVD, however. That does not mean they will be able to. Furthermore, even if the DVD's are only "available" through certain "approved" sellers, they have no right to prevent anyone from reselling the DVD once he owns it.
Your question ultimately will not be able to answered until you say whether or not the DVD really were counterfeit or not, and you...