I say this gently but the parts that I bolded show that this really was a joint mistake in a way - because just as she might have foreseen the tumble, you clearly foresaw it too and by continuing to have her care for him you do have some responsibility. And that is OK - because we all do make mistakes and 99.9% of the time the consequences are not dire. But I think you need to own that (and your DH, assuming he knew about it). And then you all need to forgive everyone...and not have her babysit again.
That your DH is a grudge holder is hard for me to address 'cause it's something I couldn't deal with. He will have to learn to be more compassionate with respect to parenting/caregiving mistakes because there will be more ahead for sure.
I guess I see it as "not a mistake" because we've talked before, many times, about what safety measures she needs to take when they're out on the deck. That she must check the gate, can't come inside and leave him out there alone, etc. It's happened a few times before that she has forgotten, and when I've reminded her, she waved it off. She wouldn't be worried or apologetic, more like "yeah, yeah, why are you hassling me, he's fine!" So I guess I see this more like someone putting the baby in the car and not putting on the harness in the baby seat, not just once like a total flake moment which can happen to anybody, but repeatedly... and then one day you get in an accident with the baby not strapped in. And very luckily everyone is OK... but it could have been terrible. She did not intentionally leave the gate open, but she didn't intentionally check to make sure it was closed either, and there's been a pattern there. So I guess that's why I don't see it as an accident... it was more like something that was going to happen eventually. And we had had just that exact conversation -- "Mama, please you have to be more careful because even though it doesn't seem like a big deal to you someday he could be really hurt. Forgetting to close the gate could really put him at risk and if you keep forgetting it's going to happen someday, so please make it a point to double check because you love him and it's important." And she would just blow it off. My mom is capable of remembering stuff like this, she's just careless, and more focused on other things and it's been a point of contention before now.
So now of course I see that I should have stopped her taking care of him before now. The only other options we have are to ask DP's mom to watch him every day, which will be a lot for her, or to put him in daycare, which I'd prefer not to do because it's not the loving environment of home, and it costs a crapload of money. (Me staying home isn't an option, I'm the main breadwinner, and DP isn't cut out to be a SAHD.) And I didn't want to separate her from the babe -- she loves him and it would break her heart.
So that's where we are now... Mama heartbroken, DP furious. They don't get along already -- she's critical of him, he takes criticism very poorly. And he's a grudge holder.... so this will never go away.
I'm really hoping to give it some days to cool down, then discuss again. I'm hoping to salvage Christmas, even if Thanksgiving is out of the picture just because it's so soon. (Our family gathers here at our house, and DP says he won't allow her here, so it's not like I can just take the baby over to her place.) I will figure something out. I love her, she's my mom, and I have to put my foot down and not let DP alienate her because of this. I don't want to look back on his childhood and see strife there, over something that in the grand scheme is a pretty small deal. The trick will be to get DP to see it that way, and find a way to get him to forgive her.
Thanks for everyone's advice, I really appreciate it!