You are not being fair to the bird at all. Of course she seems fine. Birds, as I'm sure you know, don't show you their physical or emotional ailments, but that doesn't mean they can be played around with. These animals are incredibly intelligent and they bond for life. They are flock animals, in their natural habitat they have one another 24 hours a day, seven days a week, not one second in their lifetime do they want to be alone. That's what their little spirits tell them they need to have in order to thrive and survive. As animals of prey, sticking together is what lets them know them they're safe, and God built them with those instincts. Now she's been "safe" for two years, and you're tearing this from her. Worse yet, she can still hear (maybe even see?) her family but can't preen with them, eat with them, play with them, sleep with them, or have any of the vital physical contact that she's known. If you want a bird you can handle, keep these three together and adopt a bird from a rescue that already sits alone. Otherwise, I'd give the girl about five years before she up and dies of a broken heart or simply goes mad, and any handling she allows you do will only be out of desperation for contact on her part (please never forget, you don't tame wild animals, and no bird will always allow human contact forever).
She doesn't know the reasoning behind the loss of her family, and if she did, I can assure you she'd prefer to be cramped with her family than alone with more wing room (wouldn't you?). Please, for her sake, give them back to her. Anything else is not being done in the best interest of one of God's precious creatures.
As for the Cockatiel, birds are often frightened of ones smaller than they, not to mention parakeets are quick and flighty while tiels tend to be slow-paced. A keet's just a lot for a tiel to take in (especially three at once!), and friendship takes time. Really, though, for forty days the parakeets should not even be on the same floor - let alone the same room - as any of your other birds. And you should be changing clothes and washing your arms and face between having interaction with the new birds and your current flock.
(In case you weren't aware, if you want to be sure you can easily tell a parakeet's gender by the color of his or her cere.)
Blessings,
awashinlove