I know I must seem like a prize idiot with no self respect for even considering staying
You have a lot on your plate and you're not an idiot. Your children are young and you have a 1 year old baby on top of all this.
I presume your husband is around on the weekend? Or evenings? Go to your therapist then. Let him look after the children for a while. Because if you split up, he'll have to do so during his time with them.
It would be good for him to get a very real sense that the marriage could end because of this.
Use the weekends to get some space. Go to your sister's and have clear thinking time.
Don't let this knock your confidence.
He has the problem. It's not anything to do with you at all.
I can tell you a great number of couples are increasingly seeking counselling (in the Agency I work with) because of porn and EAs (emotional affair, no physical contact).
Sometimes it's with people they'll never meet.
I'm not so shocked, because I see it happen a lot, but 13 years is a long time. These online affairs, give people highs ... like a drug.
Like I said. ... People have reconciled from such things. It not being physical (as far as you know) is a positive. If you check out the link I sent earlier, you'll see you aren't alone in this, although that's little comfort I know. You don't have to make a rash decision and you need to tell your husband, to stop saying he'll die if you leave him.
That's unecessary pressure on you and surely he'd want you to stay, because you want to, rather than fear of him killing himself. He knew what he was doing. He knew you'd not be impressed, but as the years went on he grew in confidence and became careless. He has to take full responsibility, without pressuring you.
I'd also look into him signing a post nuptial agreement, if you stay.
But it's a massive shock and you have a lot to consider.
I'm not sure what approach your therapist uses. Many use the person centred approach, which means you are the one who has to decide what to do.