Clearly she has had some advice on how to get as much as she can from you and what to say to the court. They will lie to the court especially when there is no evidence to the contrary. Document everything. Communicate via email and text to get the conversations documented as much as you can.
I would also respond to her custody proposal and add something like the following:
"It unreasonable for you to offer so little overnights, especially after I put them to bed every other night. With that in mind it is only fair, to me and the children, to have 50/50 custody and equal overnights. It is what is normal for them"
This does 2 things. She may contradict herself in a reply in regards to the every other night issue by acknowledging it which you can show the court at the proper time. And it gives credible reason for 50/50 custody.
Me:49 W:45 M:19 T:22 EA confirmed and ended 8/2014 S:19,17 D:9,5