While I agree that I'd like Frank to be her actual dad, for my own preferences, it wouldn't be a surprise that Shannon simply slept around a bunch and doesn't even know who Becca's bio-dad is.
Could just as easily be a random guy that she had a one night stand with, met him at a party, doesn't know his name, never looked for him, etc. Shannon is a heartless bitch, who doesn't care about anyone but herself, so any selfish action is well within the realm of probability. Including, but certainly not limited to, not even bothering to look for Becca's biological father. She treated her daughters more like possessions than family, so why would she put in the effort.
Looking forward to finding out the eventual answer, though I do share your concern depending on what it may be.