20 month old injuring herself

Hi all! This is my first post --- I'm looking for a bit of advice. I have a 20 month dcg that drops down to the floor and SMASHES her forehead when she is upset. Of course, she also has a bad case of the "it's mine", so she's always upset. Her forehead is a landscape of old and new bruises. I've talked to the mom and she does this at home too. Mom is single and just disctracts her (tickles, another toy, etc) or picks her up (she says it easier sometimes). I don't want to reward the head banging by picking her up; nor do I think it's fair that the other kids have to walk on eggshells around her for fear of setting her off. Help! P.S. When she was younger she would throw herself backwards, so she's always been prone to this self-injuring behaviour.

I had a head banger once in centre care and it was horrible to see if I didn't get there in time! Mostly we would shadow and redirect before he would throw himself down but if a full out tantrum ensued we would swiftly pick him up and put him in a high chair and coach him to take deep breaths. When he was calm we would say things like "Miss Lou doesn't want any of her friends to get hurt, and banging ____'s head on the floor hurts ______. When we get angry we take deep breaths. All done hurting _____'s head."