Personally I would not interpret what your wife said as meaning she's looking for a rationale for ending your marriage. Name-calling in a marriage is, to my mind, never acceptable. Yes no doubt both you as well as your wife are stressed with 2 little kids & everything else that's going on in the world. But that's not an accuse for calling your wife names... even in the heat of argument. At least that's the way I see it. And I don't see being expected to not call your wife names as being held to some unreasonably high or unattainable standard. That's simple respect.

I had a similar sort of situation a few months ago now. I've been having a lot of anxiety-related problems (as well as some physical ones.) I'd been off all psychiatric medication for several years. But, over time, I could tell I was becoming increasingly difficult to live with. I had thought, a few times, that perhaps I was going to need to get back of some sort of medication to keep myself from "popping off" at every little thing. One day I got angry with my wife over a stupid little thing & basically "told her off", so to speak. At that point I realized I had just gone "over the edge". So I got back in touch with my former psychiatrist & got prescriptions for medications that would help me to stop being so difficult.

I don't know if, in your case, psychiatric medications are what's needed. Maybe it's individual counseling, anger management training or couples counseling... or perhaps something else altogether. But at least from my personal perspective, based on what you wrote, I would say you need to own what you're doing, take responsibility for it (as you wrote that you have), but also take the next step as well & figure what you need to do to stop calling your wife names along with whatever else may be going on. Here's a link to a short article, from Psych Central's archives, on the subject:

Good Communication in Marriage Starts with Respect

My best wishes to you & your family.