What can I do to help my 4yo stop her violent tantrum ?

Thank you for expressing your concerns in detail. Hopefully, I can provide you with some answers using behavior modification approaches to parenting your child. 

When looking at the function of behavior, it seems that your child's behaving due to tangible items and possible for attention as well.  She seems to have you guys trained very well that when she wants something, and demands it, she will continue to have a tantrum until received. I would not suggest that your hug your child during a tantrum, that is reinforcing enabling and coddling behavior.  Instead, I recommend that you put firm boundaries down.  Take away anything she wants and if she is able to have it later, tell her when and only when she calms down.  You may need to put her in her room and close the door or put her in a chair and tell her she can get out once she is calm.  She then will be able to self regulate her own emotions and she will learn that she can only get what she wants or your attention if it is earned and when she completes the desired behavior which is to calm down and self regulate her moods.  Use positive reinforcement and words of encouragement at every sign of cooperation or calmness.

It will be important for everyone who disciplines her to follow the same consequence.  If one person caves into your child's demands and gives her something she wants (tangible or attention) while she is acting out, then she is learning to have that behavior reinforced.   She will also learn to manipulate and split the caregivers against one another because one parent is allowing bad behavior.

It will be important to be consistent for at least 30 days or until she learns that she will not receive and item until she is calm.  She may also need to learn "no" as a response if she is not able to obtain the item at a later time.  Remember, you get to chose which behavior you want to reinforce. If you give her items or attention when she is acting out, you are reinforcing it.  If you teach your child "No" or "At a later time" only when she is calm, she is learning that you are in control and only positive behaviors will be reinforced.

Hope that helps and good luck!