Where to start? I will just list my questions and give a brief background so hopefully someone will be able to help.

     I am on disability from the VA and am not employed. I am married and my wife has insurance on our family including my son "her stepson".  My earnings are from the VA alone which is non-taxable. Recently my case changed from me being non-custodial parent and her custodial to shared residency split 50/50 exactly on overnights and days for our individual parenting times.
She insists on our son going to daycare from 8-5 m-f for $1000/wk and not allowing me to provide daycare free as I am not working and willing/available to do so. For tax purposes we alternate years that we are allowed to claim our son for the tax credit. I am lobbying to pay daycare directly for my 1/2 of the bill instead of adding the entire daycare amount to her side of the Child support worksheet and having child support basically pay my half of daycare. (daycare and medical insurance are the only factors to my child support as our incomes are close to equal)

1) Earned income tax credit- I have no earned income beings VA disability is not taxed therefor I do not believe I can receive the child credit on my earnings alone. But can I receive it if my wife and I file together and use her earning? Can that scenario even happen?

2) Head of household- I was not allowed to claim Head of Household when I was non-custodial parent the custodial parent had that right. Now that we are 50/50 residency who gets to claim HOH? both? neither?

3) Child care tax credit- If I am paying over 1/2 of daycare directly to daycare instead of having it included in my child support obligation where she pays the daycare bill in full with the assistance of my child support. Do I have any right to the Child care tax credit?
      To further complicate things IRS says child care credit is given to parents so they can go to work or look for work and their spouses. I do not work and am not looking for work, I have offered many times to provide free daycare but she has refused (I am safe to provide care -no Domestic violence, no drug alcohol abuse, competent, no child neglect etc). With that said are either of us eligible for the credit? or are we disqualified?

Thank you for reading and I hope someone has some answers because I am lost and my attorney is as well.