What is the Sharia ruling on dealing with a gift to a Christian wife that is suspected to be a cross? And is objecting to it considered interference in her faith?

There is no harm in commanding your Kitābī (People of the Book) wife not to bring a cross into the house, but you do not have the right to prevent her from doing so. However, it is permissible to prevent her from hanging it in the house. It is required to clarify the truth to her and invite her to Islam with wisdom and gentleness, while arming yourself with Islamic knowledge and understanding the falsehoods of Christianity. You have done well by stipulating that your children be raised upon Islam, and they are Muslims by virtue of following you, but you must take care of them and guide them so that they are influenced by you and not by their mother. It is not advisable to marry a Kitābī woman in these times due to the risks involved.