With new tax laws starting in 2018 will I be able to file head of household when my child's other parent is claiming the child as a dependent? We alternate years.

Yes. Only if you are the custodial parent and you meet the other requirements to claim this filing status. The head of household filing status only goes to the parent with whom the child lived with.  

The rules for claiming head of household will be the same in 2018 as they are now. Under the current law you are allowed to claim head of household on a child that lives in your home for more than half the year even if you are allowing the noncustodial parent to claim the child. However, you must be providing more than half of the household expenses for more than half of the year. You must also enter your child as a nondependent child in the TurboTax program.  

Divorced and separated parents can split child-related benefits as follows:

Custodial Parent: (if qualifying)

head of household filing status, earned income credit, and child and dependent care credit

Noncustodial Parent: (if qualifying)

dependent exemption, and child tax credit

Please view the requirements for the head of household filing status below.

https://ttlc.intuit.com/replies/3288637