I just want to caveat this...

Firstly, I agree the dramatics are ridiculous. She obviously overreacts and her outrageous temper is no doubt reflected back to her by her children. I have no idea if she genuinely means to do horrible things to her children or these are the empty threats of exasperation.

But you making her your "common enemy", contradicting her in front of your children and not calming her down to discuss a more reasonable punishment that you both present to your children as a united front. Is likely at the very least a partial cause for her enormous frustration.

Just from your story alone (obviously i don't know the whole situation) it comes across as you don't respect her and you've taught that lack of respect to your children. Superseding her authority and being the "friend" parent is a common cause for one parent to be disproportionately the authoritarian.

I don't know her, she could be crazy. But by your own admission she doesn't follow through so she's not actually a threat. Yet you don't diffuse but escalate the situation as the "protector" like she is a threat, without mention of disciplining in place of her outrageous requests. Although you admit there was an actual offense to cause her outbursts. Also by your own admission you talk badly about her behind her back undoubtedly to her children. Do you think that has no effect on how they respond to her requests to stop misbehaving?

You didn't mention in what way you do discipline <normal childhood offense> in place of her outrageous requests, just that you divert them. That all fits the common parenting profile (often seen with divorced parents) of parents who aren't on the same page. With one parent taking the role of friend, letting the children break rules and ignore consequences. Often making parenting a harder undertaking for the one parent who is deemed the villain.

Don't mistake this as a defense for her behavior. Trying to rule your children by fear is deplorable. But every situation has two sides and the narrative as it was presented by you denotes a great deal of culpability in your actions.