My son is going through a divorce. He and his soon-to-be ex-wife have a daughter.
The mother has threatened a restraining order against me (grandfather) if I refer to her son as "stepbrother" rather than "brother" to our son's daughter our grandchild.

My son is going through a divorce. He and his soon-to-be ex-wife have a daughter.
The mother has threatened a restraining order against me (grandfather) if I refer to her son as "stepbrother" rather than "brother" to our son's daughter our grandchild.

If her son and her daughter (your granddaugther) have the same mother (your son's wife), they would not be step-siblings. They would be half-siblings. So, technically, you would refer to her son as your grand-daughter's half brother.

But in my opinion, quibbling over terminology does not justify going to court. I think the judge would tell her to stop wasting the judge's time.

But I will be honest in my house, where I have adopted kids, had step kids and more.

If you used that terms around my kids who are all brothers and sisters to us, They would never go to your house or be allowed to see you if we had any control over it.

They are brothers and sisters and should be so in their minds, They will be family after you are long ago in your grave. I think it is very petty of you to even want to use those terms to them.