if i remember correctly, they injected gun and forced gun to kill haemin, which he had a hard time fighting the desire but he managed to control it. then they killed gun instead, haemin resurrected him again using his power which awakens the mother's ability (which is what they want) they could capture haemin and gun all these time but chose to leave them alone to let the mother inside haemin grow stronger and awaken
This "father" has his whole thing with experimenting on humans with the alien thing, so even though they were trying to get the two brothers back, the "father" was also taking these opportunities to test all kinds of things on them, biological weapons and stuff. Then, seeing how they were acting like a couple and protecting each other, the "father" changed Gun's body and messed with his brain to see if he would still be able to love and protect the MC. Gun overcame his transformation with MC's help, and they continued their journey to find a safe place to live in this apocalyptic world, but they got ambushed, and Gun was killed, then brought back to life by MC using his alien powers, but that also attracted A LOT of attention, and they ended up caught by the "father", so now, once again, they are trapped in the lab.
Obs: The "father" is obsessed with this weird alien because was we can see through the story, it was incredible abilities, so he's trying to make some kind of new humanity, but it's not working, and the only successful human that achieved that is our MC, but he's also connected to the "mother," the alien itself, so he wants to test if MC can "birth" other beings. Gun can be classified as the first human to successfully be created by "Mother" (the alien) since he died, but MC reconstructed his body, so that kinda makes him the first creation. Because of that, the "father" is also conducting experiments on him to test his limits and see how he transforms, etc.
Obs: "Father" is a creep because MC never created or connected himself with other beings using anything sexual, just using his powers (AND HE KNOWS THAT), but this fucker is asking if MC feels the need to "breed" and if that's why he was having sex with Gun, but MC explains that they did that because they love each other.

Can sm1 refresh my memory?
This is the second time they got taken by facility right?
Why did the leave them the first time anyways? After injecting those drugs in gun to make him a hybrid mutant