Regarding the genetic data, I would create these priorities.
- Try to get everyone in your mother's generation and older to test. This may be a challenge since your mother seems to be hiding something. Hiding or denying Jewish roots did occur although you do not know for sure this is the case here.
- Upload your DNA to FamilyTreeDNA, MyHeritage and GEDmatch. All are free and GEDmatch has the best tools.
- Contact everyone closer than and including third cousins. If you are lucky, one in four will respond.
Good luck and keep us posted.