Does Crimson Empress have three heads that act differently, or does she simply have three heads?
They have different personalities.
Mahri, the middle head, is the "nice" one. She's the most motherly of the three.
Rana, the left head is the more aggressive and protective mom
And Isah, the right head is somewhere in the middle between those two.
So yeah, they act differently. And they feel differently. While Empress chose to leave Shadow Chaser for Ghidorah's sake, Mahri and Isah still miss their mate. They miss and love Shadow. At least the one he was before everything turn to hell.
Rana on the other hand doesn't want to acknowledge her feelings for him and holds a grudge against him, for trying to kill their own son