I read somewhere that before people change their actions, the pain of doing more of the same must be greater than the pain of doing something different. Is it possible that this could apply to both you and H?
You don't have to stop loving your H. You do have to love yourself enough to create a healthy life for you and your kids. You don't have to tell him to leave or try to control his actions, but since you can't anyhow, you must get yourself to the point where you will be happy regardless of his choices.
I'm trying to break this down into new goals since your latest goals-- reconnecting emotionally with your H and piecing your marriage back together-- are proving difficult to achieve after you discovered he's having another A.
You wondered if you should ask him if he can continue on this way. I want you to ask yourself that question. What are your lines in the sand? Can you be happy living with your H if he continues to have A's? More men and women than you think are perfectly fine with this; I'm not judging you.
Let's get out of the forest for a bit and figure out what your goals are for your relationship and yourself. Let's figure out how to find a plan to eventually end the tears.
