I just went through this exact scenario.
I was pregnant when my fiancé started an emotional affair, which turned physical.
I'm sorry to be horrible, but I would leave. We tried to make it work but I couldn't trust him, he continued to speak to her and expected me to accept they were 'friends'. Everytime she felt crap about her life she would contact him again. I feel like once someone is emotionally with someone else there's no coming back.
It hurts and it's so hard. I cried for about 6 months, but now I'm so grateful that my son and I have the opportunity to meet someone who loves us and will make us their priority. If my family is not a mans number one priority and some hussy is then I'm sorry, he's out the door.
Being a single mum is easier then you think. Don't let that away your decision. You really need to question your personal beliefs and morals and find the balance of what you are willing to accept and ignore. I made the decision to not go against my values of honestly and trust, and personally I don't believe any amount of counselling can bring that feeling of safety back you have with a partner once they have an affair.
Sorry this happened to you OP. It's the worst feeling in the world, it doesn't stop hurting, but it does get easier to cope with and eventually you will be 1000 times stronger then any woman you know.