You really have no control over when H tells the kids about OW. So, I'm not sure what you mean by "leave it to WAS to decide on their own." They WILL decide on their own. It isn't a choice you can make.
Certainly it would be better for the parents to work together: "H, of course at some point you'll want to share your R with your girlfriend with the kids. I'd like us to collaborate on how best to handle that. I certainly don't want them to be in the middle, so it would be good if you just let me know ahead of time in a direct way. Email would be fine. My feeling is that it would be better for them if __________. Perhaps we could consult with an expert to make sure we do things in the best way for the kids. Would you be up for that?"
