Don't ask. Focus on the immediate goal. Your child in your life.
This other stuff can come later.
P.S. the situation is not too strange.
Next time you are with her and she says she wants the D.
Ask her where the paper work is? Then present to her a full schedule of a 50% 50% co-parenting plan. Alternating holidays etc... until the child is 18.
She is trying to get you to give up your rights by using your own fear against you.
Flowers always make people better, happier, and more helpful; they are sunshine, food and medicine for the soul. unconditional love is awesome!