Taxes (read description)

My husband is having an argument with his ex. They have two kids and their agreement says each one of them will claim one of the kids. And it alternates annually. So last year we claimed the boy and therefore this year it was her turn to claim him and we were supposed to claim the girl. My husband made a mistake and we claimed the boy again. She’s now freaking out and yelling at him that we need to amend our return. We think it’s not that a big a deal and she can just claim the girl. Neither child has any special needs or anything that would get her extra benefits. The effect to her return is identical regardless of which child she claims. I get that we technically messed up, but should we really go back amend our return that has been done for 2 months, or should she just claim the other child?