Page 35 here: https://www.hebrewbooks.org/58066 (38 of the PDF) says that both of Rabbi David HaLevi (the Katvan) -'s daughters came from his first, unkown wife. That includes Rbzn. Beila Babad
It is a much younger source, so גזע תרשישים may carry more weight.
In any case, Rabbi David HaLevi (the Katvan) - had another wife. According to גזע תרשישים, this was the daughter of Rabbi Shimon Katz of Rappaport, whose Geni profile I could not find.
I would be interested to hear other people's thoughts. Private User, you may be interested.