You asked:

Is it legal for my sister and her boyfriend to spank my sisters children with a belt?

Reasonsable physical punishment of children by parents is not illegal by itself, but depends on the nature of the punishment. Use of objects such as brushes and belts is normally considered not reasonable. Certainly, if the child is injured, such as cuts, bruising, abrasions, etc, by the use of physical punishment, then the punishment is not reasonable.

If you are concerned, then you should call Child Protective Services. Your name will be confidential, and not given to your sister or her boyfriend. CPS could then provide advice to your sister and her boyfriend as to what punishment is reasonable and permissible. Also, you could ask CPS what is reasonable and permissible.

Stu Shafer