Dev, I would err on the side of protecting your kids. Say something like "Look I'm only going to say this once, but it upsets the kids when you text OM where they can see you. What you do on your own time is your business, but I'm sure we can agree that we need to protect the kids thru this mess. And for GOD's sake, LOCK YOUR PHONE. NO child should have to read texts from their mother to her boyfriend."
I think this is not the way to go since the kids just inadvertently ran into W at the park. It is not like W knew the kids were going to be there and she's free to do whatever she likes with her smartphone. I would not tell W what Starsky suggested ^^ right there because it would come across as controlling to W.
I agree with Train on how to approach your kids about what they see W doing in an open and honest way that's age appropriate. You just cannot sweep things under and pretend that your kids don't notice. They're old enough to see what's going on and they're smart to know that W is seeing someone else who's not their father.
You've said no OM around you, around the house, or nearby you. This is should be between adults. You cannot control if W has the OM around the kids. I shudder to think of this!! Grrrrr.
