On one hand I think maybe I can do this, on the other I think this is the straw that broke the camel's back.
You can do this and you will do this. But you've only just found out. It's raw and painful at the moment but give it time. It's like grief and incredibly painful. But the passage of time is a great healer.
You will find your anger in time and this will take over and power you through.
But it is vital that you keep focusing on the lies, the fact he isn't the person you thought he was, he even made up a false name. He lied over and over and over. He was still lying to you when you confronted him. He changed the narrative to "maybe" looking at houses perhaps in ten/twelve years time when his daughter had left home. He lied about his parents who you've now met. He literally lied about everything.
Words are incredibly easy. It's always the actions that speak volumes.
Over the period of time that you were seeing him he presented a completely false persona. You only ever got to spend periods of 24 hours with him. No weekends away, no holidays, no whole weekends even. You never saw where he lived (well obviously not). You never met one single one of his friends. All you saw was what he selected to show you, but none of it was true.
He is not a nice man at all. Because the person that you think is loving and caring doesn't exist. It's a facade. He's behaved appallingly to both you and your daughter and his own wife/partner and child. He didn't just stumble across you at work, he actively went looking for an additional relationship on line with every intention of leading a double life. No doubt when the dust has settled he will look to do the very same again.