You're trying to be a good Mum to a 10 yr old and you've got this dickhead acting in a way that could seriously affect your mental health and happiness.
I firmly believe cheating is a form of abuse.
Whether the cheater intends to abuse or not.
He has no loyalty or integrity.
And he's not only cheated on his wife but cheated - and therefore risked the marriage - in a situation in which he has be Ike a step parent and become a fixture in a child's life ..so their life is affected/temporarily destabilised if their Mum dies what many people would do and ends the relationship.
So he not only treats you shittily, he treats your child shittily too. Destabilising their home, wounding her Mum, affecting their Mum's happiness and stability.
And, as another poster says, he's been publicly humiliating you too. On topic everything else.
You sound like you think you should/have to get over this - you really don't!
You can end a relationship for anything you choose, but this is definitely up there.
These decisions take time, not leaving immediately means nothing, you can get rid of him any time you like. Whenever you've processed all this.
Just like he did what he wanted behind your back, untill someone telling you about it restricted his "freedom".