My sister in Texas left her husband today with her two children. He has mentally and emotionally abused her. He is controlling, she has lost a lot of her hair from ragged nerves.. he does not work or put food on the table. And he has never worked , she supported him. They live in his dad's house and he spends his dad's retirement check every month on video games and he has a mental history... he always beats her on the head with the bible saying that she is not submissive to him... sometimes they don't even have running water, they do not have any transportation and etc, etc, etc, now he keeps calling saying that if she
Does not call him by a certain time, that he is going to call the police because he does not
Know where his children are. My sister left him a 3 page letter saying that she will be staying with family... can the police arrest her for taking her children out of that environment?

If there has never been a police report filed, chances are they are going to take his side and err on the side of the children. HOWEVER, if she told him where they are, he has no case and just needs to file for custody.

How far away has she moved with them?

They can not call the police for her just moving out, But she needs to file for divroce and file for child custody.

She can not move so far away that he has no right to visit.
But get a child custody order in place though t he court

Tell her to get into court and file for temporary orders. The police cannot arrest her for leaving her house. But she needs to get into court as soon as she can. If she can get an attorney asap, great, but if not the court clerks will help her with what she needs to do and help her file the right papers.