Issue between SOs’ mother and mine- need advice

So my SO and I live with our 7 day old son at my moms house. We pay next to nothing to stay here because my mother is that caring and giving, we only have a bill and housework. During L&D; my mom was my lifesaver, I couldn’t have done it without her. I labored from early afternoon to the morning the next day, it ended in an emergency c section because I was really sick and could’ve “cooked” my son due to a fever.

My SOs mother knew my mom was in with me helping me labor/deliver baby boy all night and the next day texted my SO and only asked if he wanted food (I of course couldn’t eat so it didn’t matter to me), she never asked if my mom was hungry after a night of long torture so that set my mom off. My mom no longer likes her because of that and how she’s treated me.

Here is my issue with her:

-after being told at the hospital to wash her hands before she touched baby, she still tried to touch him TWICE without washing.

-she held my son for about 15 minutes then went into the corner with her bf and played on her phone.

- I’m about 7 days PP and she has YET to text me to see how I am doing or if she could bring me or the baby anything (that’s what I would be doing)!!!

- She texts my SO just to say “hey I’ll be over that way this day. I’m planning on coming over at this time. I want to hold that baby! Let me know if that works (I think she asks if it’s okay)... she NEVER texts me anything or asks me...you know the MOTHER WHO JUST HAD HER GUTS ON THE TABLE 7 DAYS AGO!...so much for being a “family”.

She wants to come see baby this weekend, my mom is no longer allowing her over due to her rude actions. (Yes, I feel that is unfair for our child but I can’t fix it currently so that’s how it is for now). My SO knows how I’m kind of hurt by her and how my mom feels, which I can tell makes him feel like crap.

How do my SO and I tell her she cannot come over?