Moll's real mother is less character, more plot device. She comes and goes so quickly that we hardly have the chance to get to know here. And neither does Moll for that matter. Nevertheless, it's this mother who gives birth to Moll in prison and starts her life on its – shall we say eventful? – journey.
Because of her mom's petty thievery, Moll is born in prison. Her mother is then exiled to America when Moll is still a baby, and Moll grows up never knowing her. If you wanted to go there, you could even argue that it's her mother's fault that Moll ends up in that unfortunate situation with the Colchester brothers. If she'd grown up with her parents that probably wouldn't have happened.
On the flip side, though, you could also argue that Moll saved her mother's life while she was still in her womb. If Moll's mother hadn't been pregnant when she got picked up for her crime, she probably would have been executed. She "ple[d] her belly" (6) and by the time she gave birth to Moll, got her sentence reduced to exile. So, Moll's mother owes her and it seems she won't ever be able to repay the debt.
Moll's mother gets fleshed out a bit more as a character when they unknowingly reunite years later in Virginia. Moll comes to know her mother as her nice, sweet old mother-in-law, and the pair develops a friendly relationship. Of course this all goes out window when Moll finds out that her mother-in-law is really her mother.
Even then, though, we still don't get much of an idea of who this woman really is. The only conclusion we can really draw is that she and Moll are remarkably similar after all. They both have exciting but difficult lives, they both spend time in prison, but they both end up landing on their feet. Perhaps it's these similarities that lead Moll's mother to leave her daughter quite a bit of money in her will.