Hmm...I'd be inclined to go through the integration process just once and get the three, so you go up to the 4 you want. Generally speaking, I think popping the new ones on the roost at night and having everyone wake up together is the way to go to minimize fighting. However- you probably want to think about quarantine for the new girl(s), as you would hate for them to bring Violet something that makes her sick. I know opinions vary on this, but I think at minimum the recommendation is that you keep new birds separated for at least a couple of weeks, if not 30 days. You might want to search for advice here. I've never had to introduce new adults to my flock (only day old chicks who were kept separate until they were much older), so I don't have a lot of personal experience to share.
As far as eating- if you really want to spoil her and make sure she's eating enough, you might consider making up a hot mash. Mine go nuts for it and it's very easy. Take some of your layer pellets, and add a little hot water (either from a kettle or the hottest your tap will go)- in below freezing temps, just be careful how much water you add so the whole thing doesn't freeze into a solid block when you bring it out. You'll see the layer pellets start to disintegrate when you add the water- then, add in a handful of rolled oats, maybe some thawed corn kernels, some raisins, some sunflower seeds, some mealworms, some chopped up kale or spinach, whatever she likes. I try to make sure most of the mash is pellets with a reasonable amount of treats added in. I have 8 girls so I divide this up into several bowls so no one has to fight for it. With just Violet, you can probably just put in in a small plastic bowl and give her as much as she can finish off in 10-15 minutes, maybe in the morning and at night.