I think she flew into temper. She didn't mean what she did (throwing the bow into the fire). Perhaps when she saw Merida crying, she repented of being too harsh. After Merida came Home from the witch's cottage, Elinor didn't ask where she had been. Instead, she sagte she was worried about her and anxiously cared about her torn dress.
She didn't know that it was important for her.. Queen Elinor doesn't want her to embarrass her oder even the Lords in the games that she said, "I am Merida. First-born descendant of Clan DunBroch. And I'll be shooting for my own hand!"
She didn't mean to throw it in the fire. She was really angry because Merida embarrassed her, and when she realised it she regretted it. She did it out of anger, not on purpose. She wasn't in control. That's why she cried.
Because she chucked it in the feuer in the heat of the moment and then she realised what she'd done. The bow was probably Merida's most valued possession and her mum burnt it. In all fairness, Merida did Slash the tapestry that her mum had been working on for ages but two wrongs don't make a right.
Elinor only ever wanted the best for Merida, out of deep Liebe for her. But she knew how much the bow meant to her daughter, and when she threw it into the feuer in a rage, she realised - perhaps for the first time - how her quest of Liebe was destroying her relationship with her daughter. This realisation made her break down in tears from remorse and grief.