You can't both claim the same child. However:
Let me know if you need more details.
In relation to to Child Care Expenses, there is a requirements that a child should be your dependent - see IRS publication 17 page 208 - http://www.irs.gov/pub/irs-pdf/p17.pdf
There is an exception for children of divorced or separated parents, that is - if noncustodial parent claims child as a dependent, noncustodial still may claim dependent care credit. That is if your child's father is claiming the dependent, but child lived with you and you have child care expenses - you may deduct them.
The grandmother can't deduct child care expenses if the child is not her dependent.
When you said 'claim non-dependent' - it is a little confusing.
Let's say this way: If your son's dad claimed him as a dependent and took the child tax credit. You don't claim your son, but may claim dependent care credit if his father didn't claim this credit.
But you are absolutely correct.
Based on information given, you, as a custodial parent, may claim HOH status and Child Care Credit if the child is living with you and child’s non-custodial parent doesn't claim this credit.
I can't tell if the charge is correct or not without detailed information about your tax return, you may ask HRB for detailed bill and we could evaluate it if you want.