I'm currently taking a cat retention course, so I will offer what I can:
Honey is being a cat. There is a new girl in HER house, someone she doesn't know. She's curious of it, so she went to investigate and found an unfamiliar cat in her territory. Not being there to know how they reacted to each other is hard to tell if she was the aggressor or the defender.
Meanky sounds like she's not comfortable yet in the new place. Letting her have her own space, a room of her own, and letting her come out on her own term to explore is fine and the best way to do that. She needs to adjust, get use to the smells, sounds, new surroundings. I suggest giving her a nice safe place to call her own. Give her a box in her room where she can retreat to. Even something off the ground that she can go up on to feel safer, especially if there are dogs. She'll feel safer higher up. Don't corner things. She might get the feeling of being trapped then. Make sure that whatever it is is facing the door, she'll feel much more comfortable being able to see what is coming and have time to react.
As for easing the tension between Honey and Meanky, it needs to be positive. Once Meanky is a little more comfortable with the new house, try having some positive interactions with the two near each other. A play session with each cat in the same room, with someone to help play with one of the cats. Try not to get them too close, or have them run into each other while playing, that will cause unwanted negative experience. If one or the other is not interested in playing, try food. Food is a great motivator. Place dishes near each other, but not too close. Let each cat have their own. You can even use a screen or something they can see through to place between them as well. That way they can see each other, but can't actually get to each other. Once they're done, let them leave the room as they please. Don't force anything. You want it to be a positive experience. They ate their food, didn't bother each other... this is good. Hey, we might be able to get along after all!
You can even do grooming or petting with the two in the same room. Any interaction where both cats are in the same room, but not too close, that is positive will help. They will both learn that there is nothing to fear in the other and that peace can exist while they are in the same room together. This should also work to help alleviate the tension between Honey and the other cat as well. You said they "tolerate" each other. Without getting more details, I'd think it might be something similar, but I cannot say for sure.
Cats don't like change, they don't adjust well to it. Work on Meanky's confidence in the house. Help her feel like she belongs with her own little areas. Once she feels a little more like family, work on her interactions with the others.
Seilahyn - Xalyndrie - Maoli