Why not talk to Y about it? She's encouraging you to be with H so she should be aware of what that entails.
Jealousy is difficult to overcome. If she's still encouraging you to do things alone with H, I would just take it slow. Talk to her, figure out how she feels about it, then go talk to H.
I think you'll be alright if you're honest.
"Regret for the things we did can be tempered by time; it is the regret for the things we did not do that is inconsolable." - Sydney Smith
Kyle: 27 year old male
Katie (rymmare): 25 year old female
Kids: girl: 5 years old, boy: 3 years old