Ashley, I agree with a lot of what Josie said above. People deal with stress and grief in their lives very differently, and often in the only way they know that works for them. It sounds like your FI has chosen to set a boundary with his mom by cutting her out of his life and not allowing himself to be hurt further by her. He has made it very clear that he doesn't want her in his life by changing his contact information and not giving her his new #s. I do respect that he didn't drag her through the mud with her family by telling them all what she had done.
While I agree with your premarital counselor that your FI needs to address the severed ties with his mom, I'm not sure inviting her to your wedding and acting like their relationship isn't stressed will help. Forgiving someone for any abuse takes years of therapy at times, and I'm so sorry that he'll have to go through that. Cutting her out of his life probably was quite helpful to him if she was that toxic. True, family is family, but that doesn't give his family a free pass to treat him however they want. I'm also sorry that she has breast CA because if he isn't at peace with his relationship with her when she dies, that will stay with him for a while.
I am sorry that his mom's family is putting pressure on you to invite them to the wedding....because this is not about you, or them for that matter. So try not to feel responsible for mending the severed family ties in your FI's family:) If they continue to be pushy about the subject and put pressure on you about being invited, you don't have to tolerate being treated that way. This is your wedding girl, and you don't need anything dampening your day!!! He has to be the one to take the initiative with her and her family, and have the desire to do so, when he's ready.
I think the best thing you could do for him would be to let the stress put on by his family roll off of your back, and just be a source of support to your FI when he needs your ear to listen. Best of luck, and just try to remember that this isn't a stress you have to own right now....especially on your wedding day