Hi I was lurking on this late last night and came back to check on things.
OMG the total and utter shittyness of some men (possibly all) never ever ceases to surprise me. This must be a hell of a shock for you, especially as it seems that you hadn't had much reason to suspect anything before this.
I'm not sure that anything we can say will lessen the pain that you must be feeling. But you WILL get through this.
I finally got rid of my ex 7 months ago, I never had any concrete proof that he cheated (clever dick) but I strongly suspect he did and had enough evidence just going on the websites he was visiting...porn, dating, random slapper friends on social networking sites. He also had other issues debts (hotels etc), drinking, emotional abuse, etc.
The absolute only thing you can do at the moment is just get on with your life (after you've got rid of him). Also, don't keep it bottled up, the more you tell people the more support you'll get. Talk talk to family/friends. If you don't know how to tell people just text and they'll come running. It's good that you're working, speak to gingerbread re. Benefits advice.
Thinking of you...you will get through this, you will x
Also, take comfort in the fact that this other woman is first and foremost a stupid slapper and most probably deeply unhappy and insecure. You are a decent, hardworking mother. Let the shit rot in his own piss...he'll soon realise what an idiot he is 