Be careful in this statement. The Church does not have any particular formula of vows required by law.
The threefold essential properties of marriage are perpetuity, fidelity, and fecundy. The couple cannot intend to exclude any of these essential properties, but the properties themselves do not have to be included in the vows themselves.
The vows not including the words “til death do us part” is not grounds for nullity. The couple must exclude one of the essential properties by a positive act of their will. If the vows themselves do not exclude an essential property of marriage then consent is presumed to meet Canon 1096 and 1099 and 1101.
A couple could certainly do or say things that would bring their consent and intent into question, but it is not nearly as simple as you seem to be making it out here. It is certainly not dependent upon certain words being in the vows.
They do not have to “appear” in a Catholic court of law. They give their testimony in a written form.