Hello Jlh, very sorry you are here but we welcome you! First of all, have you read DR and the links Cadet posted? It's a lot of reading, but it will help you to understand the dynamics at work here.
Your H is engaging in MAJOR cake-eating. You know that saying "he wants to have his cake and eat it too"? That's your H. He wants to have his fun little fling with OW while keeping you hanging on the hook as Plan B. He will hang out there, do stuff with you and S, linger, hold onto memories (like that photo), even try to have sex with you, but he will not come back as long as you let it persist because he'll be content to keep a foot in both worlds.
Here is the best thing you can do- stop the cake-eating. Tell him you need your time and space. Tell him you don't want him hanging out at your place, you don't want him pretending to be part of your family when he has chosen not to be, that you do not want him close to you when he is engaging in an affair. Tell him if he changes his mind then you are willing to listen to him and discuss options for working on things, but until then he needs to stay away.
I know that probably sounds difficult and it will no doubt hurt you initially, but believe me, the cake-eating thing is death by a thousand paper cuts. At least this way YOU take the control back from him, YOU control your life, YOU are calling the shots.
