Thanks everyone, all this advice is really helpful.

When she says "safety concerns", what she means is she wants me to go to counseling, attend classes, and write out safety plans and updated journals and hand them to her. And then she might give me one more night every 2 weeks. It is over the top. I am prepared to defend myself in court if needed. I would rather do that than accept her proposal of "every other weekend" dad and live with the regret that I didn't try harder.

I just can't tell if mediation is doomed to fail given this atmosphere. She only stands to gain by dragging this out... staying in the marital home which I pay for, not going back to work, maximizing her time with the kids. Whenever I get mildly assertive, sure enough she raises "safety concerns" again...

Ugh...

My L, who support mediation and is generally non-litigious, suggests I file the petition and file for temporary support orders. I'm a newbie, apologies if I screwed up the terminology.