If your wife has a lawyer, you need one too. Its just not an option not to. And dont ever, ever meet with her lawyer without your own.
Lots of men fall into the mental trap you are driving straight into: "if I give her what she wants, placate her, do anything I can to help her she will appreciate it and want to stay married, or she will not be angry and will want to stay married". Then you walk into mediation and hand over your kids and your future earnings to her and her future husbands/boyfriends with a smile on your face.
This might make some sense to you in your view, but her view is that she is getting a divorce no matter what, and the easier you make it for her, the better that decision will seem.
The reality is she is driving this decision, she is way ahead of you, and you are going to lose the house and kids and end up paying her half your paycheck. She will sure be happy then! Giving her 9:5 custody now guarantees she will have at least this much, probably more. You have set a precedent of giving up primary custody of your kids, men cant afford to make such a huge mistake as this. You have to remember that anything you give up, that and more is gone forever.
I really think you need to not do any more mediation, because you are going to make concessions that you will regret the rest of your life. Right now she just wants you gone more than anything else. You cannot control whether you two are together or not, so right now you need to frame your thinking that separation is inevitable. But you can control what she has to give up, and what you can protect so she can have her space. Staying emotionally strong, financially secure, and with equal rights to your children are the only goals that are within your control from this point on.