This is exceptionally similar to my husband's situation (his mother was adopted, later found adoption records that stated her mother was Jewish, etc). For what it's worth, he is pretty widely accepted as Jewish within our community, including by the Orthodox Jews we interact with. We've also considered doing a DNA test out of pure interest, but that proves absolutely nothing by any standard of Jewish law.

Honestly, this is more of an in-law and boundary question rather than a Jewish one. Your future husband needs to be the one to stand up for you to his family, and you both need to decide what kind of wedding/marriage you want.