2 important points i feel the need to elaborate on:
You get Cooch/Merc Girl anyway if you recruit the mercs, but it's also a good idea to get her before so you may do the Heist with Mina to get more Gold.
Cooch is not a prerequisite for the success of the heist event. In fact id argue against taking her to your lair at all, because doing so wastes a full day, which you need to otherwise maximize your playthrough
(im an OCD minmaxer, esp. in this game). You can still follow *and* screw her for a charm and potency point, but then leave and she'll join with rhyll anyway.
Mina either starts pissed off or neutral, but she will always become pissed if you ally with the Mercs.
Best way to deal with this is recruiting Mina and going through the heist first thing. Use charm option to get 1 treasure and imprison mina. That way you can recruit Rhyll with no problems, then use the kobold-dress event that usually happens 3 days before Maelys' attack to get Mina back to a happy status and keep the mercs on payroll.
Additionally, a happy mina who is promised bastion increases kingdom prosperity by 1 point