You moved the new bird directly into Pepito's cage? I bet he feels a little insecure, worried, and like his territory is being invaded - all this will make him feel upset and result in bitieness. Poor bub's worried. He should calm down once he sees that he mustn't be afraid but I wouldn't house them together until they're friendly outside of the cage, personally. Hidey hut's can be dangerous just because birds can easily ingest a fatal amount of the stuff by chewing on it.
Also if he's been alone all this time he will have a really hard time adjusting to having to interact with someone of his species. And if until he now he felt bonded to you you will find him acting aggressive and frustrated with everyone. First off with all the new things going on he will feel unsettled and feel like he has to protect you from other potential suitors (new birb and your kids) but at the same time he feels drawn to the creature who looks so much like him. So he's frustrated and doesn't know who to turn to or trust. (I might be overstating; he might not be as upset as I'm saying. I'm just going through much the same thing with my Damien who was raised without much contact to birds and he bonded to me. Now he's being encouraged to be with other doves and it causes frustration and aggression to me, other people, and other birds. It's confusing for them but it's the right thing to do to get them more used to being with other birds. It was a huge mistake on my part to raise him the way I did, but I didn't know that till now.) Give him some time to adjust and learn how to talk to your new little one. Personally, I'm trying to not handle my Damien as much so he doesn't feel like he's my mate and has to protect me from other suitors.
Also, I don't have that much experience with biting that actually causes damage but something stood out to me from what I've read about dealing with biting... You say you don't react to bites. Does that mean entirely no reaction? You gotta remember that the bite is him trying to tell you something. If you just ignore it you're forcing him to keep trying to tell you and then the bites will only get worse. You should be able to see what he's telling you before the bite comes, but if you can't just remember that you want to avoid the bite. Not just stay there and ignore the fact that your bird is trying to communicate something.
Your new baby is just gorgeous. I love Linnies <3 Best of luck with him!