Unfortunately my ex-husband and I had joint custody and he was not involved in either of our kids lives. When I hadn't heard from him for about a year I decided to go to the Courts and ask for sole custody. I had to hire a private detective to track him down...I've learned several things....
one, the Court doesn't care if she doesn't have a relationship with your son, the Court only cares that she is his biological mother.
the Court would always take my ex-husbands side because he was a better lier then me until I hired a really good attorney.
two it really doesn't matter if you have sole custody or joint custody because in the end the Courts will require visitation and joint decision making/raising of the child.
I've learned the important role (and become to appreciate it) that a biological parent has even if it is only once a year.
I've also learned that it is really important to show your son how adults can get along (be adults).. be flexible with shuttling back and forth especially when you are dealing with someone who sounds irresponsible.
what does matter is that you are mindful of your relationship with your husband and son(loving him without manipulation or guilt of becoming closer to his mother)
this is going to sound horrible and impossible, however have you and your husband thought about reverse psychology? meaning starting to open yourselves up to her instead of fighting? try inviting her over to a park to play with your son for maybe an hour once every few months just to get started, invite her to other public outings that your family might participate in like story time at the library....maybe this will take some of the fuel from her fire, and allow her to see without anger where you and your husband are coming from and end some of the legal stuff...
both my husband and I have done this with our ex's and they both have settled down and basically backed off. since our kids have seen us open up and encourage the ex's to be involved in the kids lives (and the ex's are not capable of doing it), it has given the kids the message that we have tried (and will continue)to have them be a part of the kids lives. it shows that their biological parents love them, are immature and not able to be an every day parent...without us having to explain or share negative feelings with them, they get it...
try to stand back take a break from the fighting and trust in the truth surfacing.
good luck