My exwife became disabled and collects Social Security Disability Benefits, our daughter was awarded survivor benefits. My exwife does not give her any money from her check nor does she spend any money on her as, I have our daughter 100% of the time and pay all her expenses. Is there a way to contest this at the Social Security Department level?

No, your not going to be able to contest it as it is part of SSD. What you can do is explain to them and show them your court papers that state you have primary custody. Then they can send the checks to your house and your daughter can recieve the intended benefit from them.