I'm sorry your sister is so troubled. Getting her committed on a 72 hr hold may not turn things around, as much as you are hoping. What happens after the 72 hours? Also, forced medicating is not so easy to achieve as you might think.

While she is in a psych facility, if she becomes disruptive, a doctor can order an I/M dose (shot) of a major tranquilizer, like Haldol, should she refuse oral medication. But what will your mom do at home?

Eventually, if your mom is going to have any kind of a life, it may be necessary to get your sister placed in a group home. However, I don't think these sort of places are locked down like jails.

I would recommend that you see if your sister might be interested in applying for SSDI/SSI. That might be a motivator to get her to allow formal psych assessments. In the meantime, your mom might tell your sister that a condition of her staying at your mom's place is that she get appropriate health care.

It's a tough situation. The next time she becomes unruly, you or your mom might call the police and ask that they take her for a mental health eval. If she's clearly been acting up, I think the cops would be willing to do that.