I agree with the previous answers. Moreover, you did the right thing. It is Father's Day. Let him enjoy time with the child and let the child enjoy spending Father's Day with his/her father. Sometimes, it is best to overlook formalities and technicalities. Your child benefits.
Here is my opinion on this subject: http://www.duthelylaw.com/1/post/2013/06/divorce-and-teenagers-minimizing-the-trauma.html
If you and your wife have split up and she is threatening to move to Boston, you should immediately go to the Nassau Family Court located at 1200 Old Country Road in Mineola and file a visitation petition. When you get a visitation order (temporary or final) make sure that the court includes the provision that mother is not to relocate out of the jurisdiction without getting permission from the court. Although that is the implicit rule anyway, you want the order to explicitly include that...
Based on the information you've given I, too, would say no. You given occupancy of the home to your wife. While you may not like it, she is entitled to have a guest in the home.
These days, a divorce based on "irretrievable breakdown" is as easy as crafting a separation agreement. Unless the two of you want to work on repairing the relationship, why not just make a clean break and file for divorce.
Although th person who received the OP can file a petition to withdraw it (I had such a case recently), judges are reluctant to do so. They suspect that there may be coercion. Even if the OP is vacated, the finding remains. There is a DV registry and a record of the finding will remain on it.
I agree with Mr. McGrath. The only answer that can be given is that you should consult with a family law attorney and determine how best to proceed. At this point, it seems like she is trying to strip you of any right to have a meaningful relationship with your child. She is probably already coaching the child to say that she doesn't want to visit with you.
If you have primary residential custody, then you should file for child support. with the income disparity, she will likely pay a fair amount. It sounds like she will be able to afford counsel---who will do his or her best to frustrate the process and overwhelm you with discovery demands if you are representing yourself. It would be wise to hire an attorney. If you absolutely can't afford one, get all of you financial documents and paperwork in order. Set up a nicely organized notebook or...
Joint custody is out of the question since he and your mother are separated and not on good terms. Further, he lives in another State. As for visitation, he doesn't really sound like a candidate for it. If his lifestyle is as you've described, I don't see a court granting him visitation.
Whatever documentation that you have to provide for purposes of your divorce settlement would be prior to remarriage. Once you are divorced, unless you file for a modification, you would not need to produce any joint tax returns filed with a new husband.
The child support will have to be recalculated based on the increase in salary, as well as the fact that one child would be living with you. It all depends on the numbers, so it is hard to give a definitive answer. If you go to the Child Support page on my website, there is a basic child support calculator. Plug in the numbers and see what it gives you.