I am not a lawyer, but I am divorced and have some practical experience with custody and visitation issues. Here is what I know:
1)Visitation rights are different in each state. Normally the state of residence where the child lives is the state law that will take precedence. You need to talk to someone familiar with custody laws for that particular state.
2) 'Grandparent's rights' is a relatively new and very fast-changing type of family law. New cases are being tried and new precedents being set all the time, which makes it a lot harder for you to know exactly where you stand. but- it also means it can be more open to new interpretation than more established laws.
Ok- here is what I would do:
1) First - I understand that you love your brother and I am so sorry for whatever he went through that has caused him to have issues after coming back from combat. But- SOMETHING must have happened that scared his wife badly enough to make her feel so strongly that she and her baby are in actual danger from him.
I am not saying she did not contribute to the situation or could not be more supportive and understanding- but this didn't just happen out of nowhere. Whatever occurred, it was serious enough that a court agreed that your brother might endanger his child.
Also- again, I am not trying to be judgmental here at all- but based on what you say above, your mom is not making the best decisions to help your brother get his life back on track. Going to a bar with him and enabling him is not going to impress a judge or help him or the rest of his family get to see his child anytime soon. Honestly- it just sounds like a bad situation and I wouldn't want my child involved. Think about if it was your own child and ask yourself, as a mom, what would you think?
You need to convince your brother's wife that you and your other family members are more responsible than your brother is currently being. That you want to have a relationship with your niece out of love and family feeling and not to try and get her on her daddy's 'side' or anything like that.
Again- trying to be honest here- what you have said above, that the mother is no sweet angel and is controlling and vindictive- it really sounds like you have serious personal issues to work out about this too. When you feel so strongly about someone, it is hard for them NOT to notice that. If I knew that was how you felt about me- combined with being afraid for myself and my child and scared of my husband- I would probably avoid the whole family too.
You need to really examine whether or not you can get over your personal feelings about the mother and try to see things in a reasonable way. You need to make it clear to everyone that this is about love for your niece and wanting to have a normal relationship with her- regardless of what goes on with her mom and dad's personal relationship. If you can't do that, I highly doubt any judge is going to help you out.
That brings me to my last bit of personal advice: seek mediation. In most divorce or family law/custody issues now, the court will often tell both parties to engage in mediation to hash out their personal issues, schedule conflicts, etc. so it doesn't waste so much of the courts' time. It can also be a much friendlier way to do it and it is MUCH better for the kids, IME.
Stalking your brother's wife on FB- and it is sort of stalkerish!- is NOT the way to get in touch with her. Again, if you are SERIOUS about this process, you will have to do things through normal channels.
If you cannot just call this woman up and request that she meet with you and your mother and a mediator to work out some way for her daughter to see your family that will not be in violation of your brother's court order and that will be acceptable to ALL parties, then you will need to go through her attorney.
Just send him a formal letter requesting that she meet with you and your mother and a mediator for a session to work this out because you want to have a familial relationship with your niece, no matter what the situation is with your brother. It is VERY likely she will advised to attend mediation- because you are being the reasonable people, asking to sort things out like grownups. Courts like that, and her attorney knows it will make her look stubborn and uncooperative if she refuses to even meet with you in mediation. This will only work if you commit to going to a mediator though- she can totally refuse to call you or meet up for coffee someplace- it is NOT the same thing.
You MUST stress the difference between your brother's behavior and actions and those of your family. And everyone in the family must stick to the rules. If she agrees in mediation that her daughter can come over ONLY if your brother is not present- then you MUST abide by that.
Tell her attorney that they can choose the mediator- it won't matter who picks them, as long as it is someone court-certified. Usually mediation is about $200 per hour- cheaper than an attorney!
Usually each side will meet privately with the mediator first to discuss goals and issues and they will help you figure those out too. Then you will all meet together. It is AMAZING how helpful it can be to have an uninvolved 3rd party to help sort things out and get everyone to compromise a little. You could work it out so your mom and dad get to meet them at McDonalds and take your niece to the Playplace, or at a park or whatever, until everyone is comfortable with the situation and then have meetings at home.
The mediator will write up what everyone agrees to as a legal document to be filed with the court as an addendum to your niece's support and custody arrangements. Then everyone must abide by it- or arrange to return to mediation to negotiate or talk over any major changes. Having that as a guideline really helps everyone to stay on good behavior.
You will have to give a little to get a little. but in my experience, it will be WORTH it. At first it is going to be awkward, but everyone will get used to it and if you all stick to the rules, you will all be glad you worked this out as your niece grows up. Although I did not get along with my former MIL when I was married to her son, I knew how important she was to my little boy and how much she loved him. She is much more elderly than my parents and lives in a retirement community. I made a point of taking my son out regularly to see her and stay with her and now we have a GREAT relationship. She and my son are very close and I am so glad he has had that in his life- but it could have easily been otherwise. You need to work WITH your brother's wife, not against her if you want to make this happen, no matter how frustrating it might be.
Oh- and don't worry about her snowballing the mediator. Those people have seen and heard everything- they are very good at sorting out truth from fiction and, in my experience, very fair.
Good luck- I hope your brother is able to get the help he needs to recover and that his wife can see that her daughter will benefit from a relationship with ALL of her family so you can all heal and move on.