OP, you say that you are unattractive and reference your insecurities about him wanting to sleep with more attractive women. Accurate or not, it is a terrible feeling and puts you in a terrible mindset. You deserve better and should endeavor to treat yourself better. 
I want to help you get to the root of your feelings because you're obviously very unhappy. I think the focus on your husband in this thread is misguided - you need to be centered here. Regardless of what he is or isn't you aren't compatible anymore so I think you focusing on you is your best course of action.
We are all responsible for the outcome of our choices you chose to marry him and it didn't work out. It was a choice you made... no one makes great choices all of the time and no one ever has every shred of info prior to making all choices. You didn't know that he engaged in something you find detestable prior to marrying him, now you do and it created a vast divide between who you believed he was and who he is. And that my dear is really fucking shitty. It sounds like it killed your marriage and understandably so - I'm sorry for your loss. But much like the death of a spouse the death of your marriage shouldn't be the demise of you.
Now it is time to make new choices, choices that put you at the center of your universe and holds your children close. You deserve to be happy and to obtain that happiness you will have to make some very hard choices.
You want to model behavior for them but also they can feel it if you're not happy and they can see it no matter what you think - seeing you sad will make them sad.
Have you had a convo with your husband to discuss the climate of your marriage? If not can you approach it in a way that he will engage without fury? I know it is very scary but if you don't fear violence from him having an open conversation may be the first step in opening your path to freedom. Sometimes what we think we know and reality are much different. Maybe he feels similarly (i.e. marriage is dead) and would be open to dismantling the relationship for his own happiness? You won't know unless you ask (if you have gone through all this my apologies but I try to not assume anything).
I recommend you begin seeing a therapist to deal with your insecurities and to help you find a way to love yourself. We all need an objective sounding board sometimes so please don't take the suggestion as a dig/judgement. You can find a therapist online they can do web chats since your schedule sounds quite tight.
Please seek therapy and begin to create your new path without your husband, you can do it - don't tell yourself you can't. Your children believe in you, we in FWR believe in you, now you have to believe in you.