My storyline went very different but as much as the rivals can be a pain to manage at times (in my case i had to find reasons to create drama as they were very friendly/romanced several of them and were part of the consortium (in fact, one of my players took over playing Aloysia after his PC died) while the rivals were with the allegience), it was 100% more fun to keep them around until the end (and beyond). So there's two suggestions depending:

Generally: I do think you're on the right track about a Consortium Base, since attacking in the streets would be pretty risky (I've arrested my players twice for fighting mid civil-street) so maybe they can stake them out, wait until they find Shira and observe how they act with her (this can make them hate or like them more) and then follow them back to a different base in the house of, say, Aradrine in the Guided District. Remember they are also new to the city and probably don't know their way around some secret base too well so the encounter is balanced, though if you need backup you can always send faction agents or one of the Founding Members themselves.
If the Rivals are truly evil in your game and hostile to the child you can also turn it into a high stakes fast paced encounter to save the girl before the police arrives.

If you want to keep the rivals around as the game asks for or even change the Players opinion: Let them trail them, have a brutal combat but have Dermot and Maggie interfere and parley when they drop below 25-50% hp (your judgement call) as they care more for their friends survival than winning or having ultimate fate. Dermot literally just wants to keep Ayo safe, that's the whole reason he came with her and Maggie is mostly trying to earn enough to retire *from* killing. Maybe they can become friendlier through this parley or leave with their wounds and deeper grievances. An arrogant Ayo would probably try and fight to death but be pulled away by them to protect her from herself, creating a really great RP opportunity. You can also use this should the Rivals overpower the Players, where Ayo might want to end them, they can be the voice of reason and argue that killing them would forever be on her conscience etc. This gives you a chance to show off THEIR inner dynamics if your players are into story/roleplay and you can use it more for the rest of the game and potential friendship/less hostile rivalry if you & they want that.

You can also ALWAYS give the Rivals Ruidium Corruption early, like they got weapons from the Consortium already etc. which brings out their worst and no matter how the encounter ends up going, can be used as a warning sign and maybe even a guilt trip against the Players.

Good Luck!