Keeping baby away from mother in law. Any advice or input?

To start off this is why:

-it took my husband and I 8+ years to have this baby due to infertility. The whole time she just pestered ME that I was prioritizing my career over family, and when my husband disclosed our issues she never apologized or even acknowledged what was shared. She went on like nothing. Which was hurtful.

-When we finally got pregnant and announced it to them FIRST. She didn’t even want to look at the ultrasound photo flipped it upside down. She said ‘finally’ and she expected to ‘have a lot of grandchildren and no one has been delivering on that behalf.’

- I ended up in the hospital for days at 28 weeks pregnant and almost was sent into an emergency c section. She never called us or even asked how we were doing or the baby.

- she has never called or when in person even asked about the baby. I have offered to show her pictures etc. She’s declined.

- She didn’t come to the baby shower nor even sent a gift. She lives 10 mins away from us.

I asked my husband about this who said his mom made it very clear to us that she doesn’t care for him not this child and that he doesn’t want the baby anywhere near her.

The baby should come any week now.

My question is how do I nicely tell her we don’t want her near the baby. As knowing her for 10+ years the only time she will show the baby attention; want to hold him and take pictures, is when she has an audience of her friends. I want to respectfully tell her no and why and I KNOW we’ll have an audience and don’t want to depend on just my husband to stand up for the baby and I as he can be very brash to her due to how upset he is with her behavior or in case he is not present at the time.