I'm not sure why you are so adamant to talk about separation, I saw that you mentioned discussing it with your coach but I don't have all the details. Are you wanting to separate and divorce your wife? If so, why wouldn't you take action to make that happen? Talking about it shows how indecisive you are about it.
Every LBS here says that their WAS is the stubborn and will not change their mind. Well if she was so set she would have filed for divorce already and been walking that path, not throwing mixed signals. Don't let things like this trip you up. This is where it pays to be detached, to have a clear mind.
Also, every LBS, including me, has hoped doing "something" will "bring her to her senses". But it's the doing nothing that will ultimately make her reconsider. Get out of her way. Stop dancing to get her to change her mind. Stop worrying if she'll change her mind. Start doing attractive things. Stop blaming this or blaming that. Blame yourself for what you could have done better and leave it at that. 90% of people are great at blaming others and dodging responsibility for what they did. Own your crap and fix it. The best apology is changed behavior. And quit verbally apologizing. She stayed together for the kids for the last 4 years and you apologize? I don't get it. You make yourself look bad and miss and opportunity to validate.
I am a firm believer in the LRT. Stop pursuing, GAL, wait and see. It is so simple and you W has qualified you for LRT. MWD says you should LRT when your spouse says they want a divorce and they are serious. So here you are, time for LRT. Telling your spouse about kids in 2 houses is pursuit. I don't read about any GAL or waiting and seeing. Seriously, take the pressure off. Take this time to brush up on 2-3 validating phrases. Stop inputting your thoughts when she isn't asking for. Read about good communication. Learn some new skills, restart old hobbies. You can do this and if you truly believe she is sending mixed signals than you HAVE to because it means she doesn't know what she wants. Quit focusing on what you can't control (EA) and focus on what you can. Don't take her bait. She is going to $h!+ test you. Are you strong enough to hear some annoying crap and not let it get to you? Can you pass the test?
H 34 W 29 BD 3/12/18 Divorce Busted Spring 19
It is not things that bother us, but the stories we tell ourselves about things.