Separated for full year

What is the name of your state? IL

My wife and I have been separated for the entire calendar year. Our two children have lived with me for the entire year and I was officially awarded temporary custody of them in July. She contributed nothing towards support of the children until she was ordered to pay support and 40% of non-reimbursed medical expenses (also in July).

My question is: Am I within my rights to claim the both the children on my income tax return? Nothing has been argued in court about this and my instinct says to just do it and fight about it later if needs be. Another option would be for each of us to claim one of the kids. Would this make a significant difference in my refund amount (generally speaking, of course)?

Thank you in advance for any help or advice.

You file head of household & claim both kids and EIC, if applicable. As custodial parent, you get the dependencies unless you give them to her.

Thank you VERY much for the information.