The key things to mediation I was told is, it takes two reasonable people to come to the table (as KML said) and the mediator’s sole goal is to reach an agreement. They have no skin in the game but to reach a resolution so by nature if one of you is firmer/more resolute the mediator will whittle down the one who says uncle faster to meet the goal of resolution.
I did not bother with it because I knew my ex was not reasonable (he wanted to pick how much he paid in support rather than following state guidelines and he is definitely more resolute about not breaking down). Your wife is clearly manipulative and using scare tactics. Don’t agree to less than 50/50 because you deserve that and you will pay more if she gets more custody!
If you go to try mediation, I would have a list of absolute non negotiables that you reference frequently and go into it ready to walk out. You can always try again! Have your L on standby.
You are here in this position to overcome her control of you, your fear and to take what you lawfully deserve. Go to the mats and take what is rightfully yours. Your kids needs 50% with you!
Last thing, as she wants to work one day/week and stay in the house, make sure you take the kids promptly every day you have them and document this. I speculate she is making a case that she deserves more than 50% due to your work schedule while she is still the primary care giver working minimally (and conveniently) living the same lifestyle!!!!
Me 41, H 47, M 15 yrs, S11, S13 BD 1: 11/4/14 we work on it; really I pretzel myself BD 2: 3/31/15 H goes down to "dorm room" 8/15: H back to MBR 10/15: H back in dorm room 1/18: H files, now divorced