When Frigga was told of Loki's "death", she forgot her composure and dropped to the ground. She screamed, she cried, she shook, she lashed out and hit and kicked and cursed anyone who dared get near her. She had lost her son, her youngest son, her favorite son, the son she hadn't really birthed, but had nurtured, watched grow, loved.
Just as he had "fallen" into Oblivion, she had "fallen" into depression and despair. She wouldn't eat, she wouldn't sleep, she cried for him, begged for him. When she had finally mustered up the strength to leave the palace walls, she stood at Heimdall's side for days, asking, inquiring, pleading for him to tell her if he could still sense Loki's life, Loki's presence. It was all she wanted, all she hoped for.
When word reached her ears of his menace on Earth, she cried more than she did when she first lost him, though not out of anger as Thor and Odin did. She cried out of happiness, joy, wanting and needing. He was alive, he was breathing, she would see him again, touch him again, hold him again.
Despite all that he had done, all of the innocent lives he had taken, all of the ruin and panic and pain he had conflicted, he was her son. She wouldn't lose him again.