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I am sorry to hear about the problems you are experiencing with your daughters. There seems to be quite a bit of anger between the two sisters. It may be helpful to consider what may be contributing to this (perhaps jealousy). It is important to be careful not to encourage this jealousy by fueling the conflicts or taking sides. However, it is also important to set limits that violence is not acceptable. Threats, particularly to kill another human being, are serious and should not be ignored. The message to your daughter should be that this will not be tolerated. If you believe that these threats are plans, then hospitalization may be needed in order to offer safety for both girls. However, if you believe that this was not a serious threat, then individual or family psychotherapy may be very helpful to address the issues that are contributing to these conflicts. Strangling is not something to be taXXXXX XXXXXghtly and should be addressed by a psychologist.
You may also want to let your 20 year old daughter know that if she continues to engage in physical confrontations with her younger sister she could be charged with child abuse and to tell the 17 year old that if she continues with physical conflict and is out of control she could be hospitalized. You can also let them know that if they become physical again, you will call 911 in order to set a limit and protect them from harm.
I hope this answer is helpful. Please let me know if I can clarify further.