Is a pregnant wife's travel in the first trimester for 'Umrah, using her second nationality because travel with her first nationality is impossible due to a foreign country's system that prevents her travel in this situation and there being an issue with receiving the necessary vaccination, considered harmful or forbidden from a religious perspective?

The 'Umrah is obligatory once in a lifetime according to the most preponderant opinion of the scholars, but its obligation is conditional upon ability. If performing 'Umrah would harm the pregnant woman or her fetus, based on the report of a skilled and trustworthy physician, then she is not required to go until the impediments are removed. There is no harm in traveling with one of the two nationalities if she holds dual citizenship.