I’m sorry, but I think you are doing the wrong thing lying to your children. I am not a psychologist or a psychiatrist. But I have extensive experience in working with children who have to be told much more difficult and traumatic things than the fact that their dad has a GF.
In my field we always encourage parents to tell the truth in an age appropriate way. This is especially true when it’s the children’s information that they have a right to know. Sometimes it can be hard tO know where that boundary is between their info ( that they have a right to ) and others people’s info ( which they don’t ).
It seems very unkind to let them believe that he left because he preferred work to them. They need to know that its not their fault in any way .
If I were you I would sit them down and explain that you have to talk to them about your dad. That you hadn’t told them this before because you wanted to protect them . But now you realise that was the wrong decision.
That their dad left because he met someone else who is now his GF. That you’ve never met her but her name is Jane and she works with their dad / whatever.
You dont need to defend his actions or pretend that its ok. You can say that you were very sad and upset because you expected to stay married to him and be happy, that splitting up wasn’t your choice. But that you can’t make him stay, the same as the children can’t make him stay. He gets to make his own decisions.
They may ask questions that you don’t know the answer too and that’s fine , just say that.
Or you may know but feel they don’t have a right to know eg was dad having sex with her before you separated. And you can just say thats up to their dad if he wants to tell them that.
I’d expect them to be angry but thats fine. They are allowed to be angry and upset.
Please do not tell that how to feel or think, they need to be allowed to deal with it in their own way. And if that means their father has to cope with their reaction, thats ok too. If the 16yo stops seeing him for a while, that’s their choice. People have to live with the consequences of their decisions.