Even though she does not have an annulment for her first marriage, my non-Catholic sister-in-law married a man (Catholic, albeit the cafeteria variety) last Friday… at the courthouse. They got married because she’s pregnant. So, do I recognize and consider him my brother-in-law?
Given the circumstances you report, the Church would presume that the marriage is legal (i.e., recognized by the state) but invalid. As to whether you can consider your sister-in-law’s husband to be your brother-in-law, the Church does not forbid you from doing so. In our society, we tend to be rather free with designating family relationships even with those to whom we do not have biological or legal bonds. Given that you do have a legal bond here, and if it would preserve family relationships at a time when your sister-in-law appears to be doing the best she can to provide for her child’s future, there would be nothing wrong with considering her husband to be your brother-in-law.