Is my insistence on hosting my maternal uncle and his wife in my home, despite my wife's objection, an injustice to her, or is it my duty towards my family, especially since my maternal uncle's wife is my wife's paternal aunt?

The ruling depends on determining the ownership of the house and furniture.

If you are the owner of the house and furniture: Your wife is not allowed to object to your relatives staying there in her absence, because the house is your property, and your action of hosting your maternal uncle and his family is an act of maintaining kinship ties. The wife does not own the house; she only has the right to reside in it. If she has a private space whose privacy would be compromised by others seeing it (like the bedroom), you can lock it.

However, if the furniture belongs to the wife: You are not permitted to host anyone who would use this furniture without her consent.

And if the house itself belongs to the wife: It is not permissible to allow anyone to reside in it without her permission.