You can GAL with the kids also. Take them to the park, find something to do with them. I'm not sure how you would handle going out without her since you two aren't in the same situation as I was. I could take my kids and go out and W would just say "ok" when I told her I was leaving. You might just say "I'm taking the kids to XXXX, you're welcome to come if you want, were leaving in 5 mins". Just don't try and use it or see it as a way to spend time with her. You might even just say your going and leave it at that.
Go out with buddies once a week or so, find something new to do.
Just don't spend every day, all day waiting around for W to see what shes doing and her mood.
You say there's tension and you walking around eggshells because of her mental state. That's a mistake, you have to keep to a PMA regardless of her mood. She can likely feel that your tense and walking on eggshels, and its not attractive. You have to attract her back, which means be content in yourself and happy. She wants to be around someone who is fun to be around, not someone who is moping about and waiting around for her.
Accept what is, let go of what was, and have faith in what will be