Angel, you can be glad she didn't ask you to leave, because if you had, she could have claimed that you abandoned the family and you could have been in a very tricky situation legally.
You should see your L asap. She has a L and a group that advises her, and she is doing legal maneuvers that you can't afford to let her get away with. You have to focus on your continued access to the children. I understand you feel like you are in a state of shock, but after several weeks, it is time to splash cold water in the face, take a deep breath, and start thinking strategically.
Talking to a L is like getting insurance. You don't refuse to get home insurance because just the thought of your house burning down is too devastating and upsetting, right? And you don't feel that getting insurance reflects on you negatively? This is the business end of things and they have to be addressed.
We need to prepare for the worst and hope for the best, as with anything else in life. I think you should send W a request to see the children and stop leaving it up to her to dictate when you get to see them. You and they have a right to see each other, and if she denies you access to them, you should go to court to get an emergency custody agreement in place. If you wait much longer, the judge may wonder why. It could reflect on your ability to take care of them, if it seems like you have to have your wife tell you what to do or that you are completely set out by circumstances and can't handle a crisis.
Again, what if your house burned down? Would you sit down and cry over the house while watching your kids wander confused around the yard? Or would you gather them up and get them to safety, like the responsible father you are? Because you realize you'd have to deal with the house later, right now you would focus on the kids. W is the house on fire right now. Somehow, try to disconnect your children from your wife. They are completely separate relationships and in this situation, they should be treated differently.
Your W is going through something you can't fix or make right at this time. And the more you try, the further away she will pull. She is an adult and can take care of herself and make her own choices. She is making some choices you sincerely disagree with. Take all your strength and focus on what you can do. And please, stop using the word 'allow' for her to see your own children. She doesn't own them, you don't need her permission.
I hope you take this as a pep talk and not as criticism. I've fought for father's rights for many years and it frustrates me to no end when I see a father believe that he has to ask the mother for permission to see his own children. It's both society and men who are responsible for this, and some men don't seem to care too much about their children after a divorce - but don't let those men set the standard for you!
Best of luck!
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17