I would honestly try to leave him out of it now and forever. You could tell her you want to clear the air between the two of you regardless of what happens in your marriage. If it appears to be a tactic to get H back I do doubt she will participate. Its more like "we both feel badly about how things have gone, let's clear the air and put it to bed."
Separate making peace with her from what's going on with H. If she won't talk to you, you tried and will always take comfort from that. I do think though that it may get worse before it gets better.
I would definitely assume that H never wants to be in the middle again and act on that basis.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015