You likely come from an emotionally healthy family yourself so seeing his mother like this came as a bit of a shock (understatement) to you.
Your DH needs to realise that his primary loyalty is now to you and his child and not his mother. His own inertia when it comes to her is really hurting him as well as his own family unit. He and you need to present a united front when it comes to his mother; you can talk at a normal volume in your home for one thing and he should make that crystal clear to her as well with you present.
You do not mention your DHs dad in all this; is he still around?.
Your DH seems to me to be as problematic as his mother is. Their relationship is certainly dysfunctional.
What boundaries does your DH actually have with regards to his mother?. It also sounds like he is completely enmeshed when it comes to his mother; she has not wanted to cut the apron strings and will not let go of him. He also sounds very much in a FOG (fear, obligation, guilt) state when it comes to his mother as well. She has made him feel extremely obligated to her. She did a bad job when it came to her son, do not let her do similar damage to the next generation.
Boundaries are what create a sense of individuality between people. And although we are all physically separate, it does not mean that we are emotionally separate from another person.
This becomes what is known as enmeshment, here one will look physically separate, but emotionally they will feel attached to the other person. One will feel that they have no boundaries between them and as a result that they are not an individual.
So when it comes to mother enmeshed men, it is describing a man who is emotionally entangled to their mother. While it is true that they may live in a different house or a different part of the country; the emotional cord has not been cut.
Never forget that you are this child's parent and you have the final say.
If your son grows up seeing his nan disrespecting you as his mother constantly what mixed messages does that send him. You need to protect your child from such malign influences. DO not let her parent your child.
Did you tell your DH what she said about your singing to your child?.
Where is she staying on her next visit and how long for this time around; it certainly cannot be in your home. She must not stay in your home, she will need to find alternative accommodation.
Re your comment:-
"My dh is an only child so being NC is not an option"
This is an irrelevant point. You can decide on what boundaries you have with regards to his mother, you can see her as little as you wish.
Your DH may want to continue to have a relationship with his mother but it does not follow that you or your son have to meekly follow suit. She sounds toxic and is not a good person to be around.
You cannot change her but you can certainly raise your own boundaries still higher. You can certainly change how you react to her.
I would also suggest you read Toxic Inlaws written by Susan Forward to further understand the power and control dynamics that are being played out here.