If the 3 members of the bet din were shomer shabbat and otherwise kosher l’edut, you are fine.
And let us not get into the kabbalat ol hamitzvot debate. I’ve made the shita of the Rambam, as understood by Reb Chaim Ozer and others well-known. And the principles of hora’at sha’ah also apply b’zman hazeh, per R’ Goren, R’ Uziel, and other brilliant poskim.
And R’ Akiva Eiger, the Maharshal, the Mahari Algaz, and many others did believe that the child of a goyishe father and Jewish mother required giyur, while R’ Uziel, R’ Kalischer and many others felt that the child of a Jewish father and non-Jewish mother still possessed some degree of kedushat yisrael because they’re mi zera yisrael.
My advice to you would be to stay away from Haredim and their institutions, since they annul conversions and declare lifelong Jews invalid all the time nowadays.