OP, you're not an idiot, you trusted your husband, he is the idiot. Please dont blame yourself for trusting and loving someone, its not your fault hes done this.
I cant help with the money side at all, but I would be onto a solicitor to see what my rights are. Surely if you were married you're entitled to something, even if hes moved it abroad.
I would fill in CMS right this second, it'll take them a while to locate him, tell them his phone number, email, work address, anywhere he may be staying. Do that right this second so then its done.
Don't contact him again (other than any legal stuff you may need to do). Don't beg, cry to him, try to appeal to a better side to him. Hes a twat and this is him. My partner left me and our child abruptly one morning out of the blue and he doesnt see our child, i am so glad I didnt beg, even though it was so hard not to!
Keep busy with your babies, cry when you need to, spend time with family and friends.
I'm so sorry you're going through this, sending you so much love, you and your children deserve so much more x