Sorry that you are in such an impossible position. I echo lots of PPs views on H, so I won't repeat it here.
About OW. I would never trust OW. Firstly any decent/sensible person with their history would never ever put themselves right in the heart of the family. Respecting the boundary and keeping distance is a sensible thing to do. She hasn't.
OW told your H or (you) that she feels threatened by her own H's continuing friendships with his ex girlfriends. So she knows exactly how an ex hanging out with your man feels like, yet she chose to do exactly that to you. She would probably defend herself that Oh OP is so cool and strong so she thought it was OK. Don't buy into that. She is inflicting the pain she received from her H's ex girlfriends onto you. She knows exactly what she is doing.
OW's recent texts to H are well thought and carefully constructed messages to the extent that they are unnatural. They are carefully written (rehearsed in her head many times) with wider audience - you and the friendship group - in mind. They are OW's public speech marking her territory and trying to prove her innocence and her high moral standard.
"Sometimes she has worn really fucking stupid shoes when we have been out and I have had to give her my arm but everytime I have told you..." (H's comments from your earlier thread)
Does this mean that H and OW "sometimes" have walked arm in arm? I guess her feet become painful magically only when she is out with H? (Have you seen her needing support from others in walking in those shoes, you or any girlfriends ?) Obviously this is not one-off case of brand-new pair of shoes causing blisters the first time you wear them, is it? If this happened more than once, it is an intentional act on her part as well his.
OW isn't as innocent as she or some would like to portray herself. I see an extremely thick skinned clever woman, putting herself in right in the middle of your life whilst knowing that the "friendship" is making you uncomfortable.
Your H. His recent short texts to OW creeped me out. Sorry. He sounds like a little boy desperately trying to get attention, approval and reaction from a mother. But he is not a little boy. He is a middle-aged man with a wife and children. It's pathetic, inappropriate and unhealthy. The power balance in their so-called friendship changed somewhere along the line. I always viewed OW as a marriage breaker. By sending these pathetic texts to OW on her honeymoon, he is stepping on her man's toes. He probably has lost perspective as to what his actions look in other people's eyes.
With all I have said here, I am not ready to join in the "LTB" group, yet. H needs to fully "wake up" from this unhealthy obsession with OW, and he will probably need professional help to achieve this. However, I would never trust OW. She shouldn't be in your family life.