I’ve got a theory here regarding the Law/Kid’s Awakenings. First off, I think that this was a pre-meditated combo attack from Law and Kid using their Awakenings. The fact that they discuss using them because the situation is now dire enough implies to me that they knew the capabilities of each other’s Awakenings.
My guess on how the powers work is two fold: (1) I think Law’s Awakening allows him to make smaller, more powerful rooms that coat/emanate from objects (like his sword) whereas they previously only emanated in a dome around him, and (2) I think Kid’s ability allows him to control the magnetism of his environment. Both line up with what we already know about Paramecia Awakenings and their ability to manipulate the environment, not just the body of the user.
So my thought on how this went down is that they knew the potential of Kid’s power, but he was unable to use it on Big Mom for some reason. My guess is that her skin and all exposed parts of her are covered in her superior Armament Haki, essentially protecting her from Kid’s Awakened ability. Law’s Awakening allowed him to somehow pierce her Haki (maybe the smaller room is more powerful? Or allowed the blade to phase through her skin?), however, and allowed him to attack her internally like an alternate form of Advanced Armament/Conqueror’s Haki imbued strike from one of the Yonko or Luffy. In my opinion this is Oda’s way of giving Law an ability that is similar in effect to Advanced Armament/Conqueror’s Haki imbued strikes without having to explicitly do so, thereby keeping Law roughly on par with Luffy and Kid (who are clearly his rivals) without it feeling like he’s just giving Conqueror’s Haki to everyone.
Once Big Mom was damaged, she then coughed up blood and Kid instantly struck with his power. I think we’re going to find out that Big Mom’s skin is coated in Haki like armor, but her blood wasn’t – aka Kid was able to magnetize her blood (or perhaps the iron in it?) resulting in the effect that we saw at the end of the chapter.
This interpretation gives Kid’s Awakening strength, but also a much needed limitation as he would otherwise be able to simply magnetize an opponent and immediately crush/immobilize them at will. Opponents at least stand a chance if they have to be either wounded before his Awakening is useful or knowledgeable enough about Kid’s power to fully imbue themselves with Haki to defend against it. As for Law, he seemed to complain about the toll that using his Awakening takes on him so perhaps his limitation is similar to what we already know about the Ope Ope no Mi, aka that using its Awakening can shorten his life span or otherwise uses his life force to power it (similar to how we know that using the immortality surgery would kill him).
So essentially I’d argue that the whole goal of Law’s attack wasn’t truly to strike a killing blow against Big Mom, but just to open up a chink in her armor and allow Kid to use his Awakening to damage/immobilize her, thereby completing the combo attack. If I’m right, I think this is going to effectively end Big Mom’s role in the raid.
*Theory by Buzzardry