Does my wife have the right to object to my sponsoring the expenses of my siblings' Umrah pilgrimage on the grounds that they are not poor, and that charity given to a poorer stranger is more deserving? And what is the definition of a poor person in Islam?

Your wife may advise you to direct your spending towards what is better, but she does not have the right to prevent you from spending on your siblings or relatives. You have the right to dispose of your money within the bounds of Islamic law.

Giving charity to the needier poor person is better than giving charity to relatives if they are in a better financial state. Similarly, it is better to spend charity on those who are in need of it, rather than giving it for the expenses of an 'Umrah (definition) for a specific person.