fun fact, the firm Laurel works at is called City Necessary Resources Initiative, which spells out "CNRI".
I do think they will show Laurel taking the law into her own hands, maybe she will find out her dad is tapping her phone or something. Plus they showed her having self-defense abilities earlier on in the show. I just think it will happen in later seasons if they get to that point, we already have Roy Harper coming on to the show anyway.
The mother black canary probably has to die first so the daughter can take over. It is unfortunate that the New 52 has a policy against legacy super heroes but Geoff Johns managed to sneak in his favorite Stargirl sister as a legacy super hero of Sylvester Pemberton and Pat Dugan.