Also, sometimes shitty moms keep custody for the financial benefit. Try offering her a buyout...
I hadn't thought of this. could be a good plan.
No mother in their right mind would ever accept a buyout. Think about what happens when that kid turns 18.
"Well, mommy used to really want you to be a part of her life and help raise you well, but daddy offered her a bunch of money up front so that you could live with him. So, yeah, mommy just saw you as a golden ticket to a couple g's but I bet she still loves you and stuff."
Hire a good lawyer if it means that much to you.
Consider yourself lucky, if you had a 15 year old daughter when you were going through a divorce, she would automatically turn out to be a hooker. 100% of the time.