1. A US court orders something.
2. The Executive Branch enforces that order, as it is responsible for the DOJ which is in turn responsible for the US Marshals (who enforce court rulings).
3. If those people do not enforce the rulings, Congress brings articles of impeachment and impeaches the President or others responsible.
4. Elect/appoint/elevate a new person to carry out the court order.
The Constitution doesn't really account for the possibility that 1/3 of the Senate would disagree with an ignored court order. So hard to say where it goes from there.