I did this on my own as my ex was too scared to do it. It was awful, I have to say.
What I did was this. They used to like to watch Coronation Street - they were 8 and 10 - and on one particular day there was a story coming up that they were looking forward to watching. He went out at 7pm. At 7.15 I drew the curtains (kids playing outside used to look in and I didn't want that) and told them I had something very serious to tell them. When I told them they were incredibly upset - they ran around the room screaming. Of course I was crying too, by then. They asked a few questions then my son asked how long his dad had had his new girlfriend and my daughter (aged 10) shouted "Don't tell us!" That was a good idea. I really don't think they want to know much.
Then after 10 minutes of them being upset I said, "OK we've done enough crying now - it's nearly time for Coronation Street." They brightened up and then their dad came home - more tears - and I said, "Come on, it's starting" and they sat on the sofa and within two minutes - literally - they were laughing at what was happening on the TV and didn't cry again.
So my advice would be to set a deadline on the pain by planning it in a similar way. Make sure there's no-one else around. Have a treat planned - at half time on Corrie I "remembered" we had Ben & Jerry's in the freezer. Don't expect them to do normal things later in the day eg visiting someone.
FWIW a few months after he left, my son said "I know this sounds weird, but has Dad left?" So much for his presence in the home, eh?