That tang doesn't look healthy at all. Regardless of whether you pulled her out of the main tank as soon as you noticed it or not, there is still ich in the display. Even if the tang was 100% ich free now it would just get it when reintroduced back into the main tank.
That being said, ich CAN be controlled by good water parameters and a stress free environment.
What other tank mates are in the display?
What do your nitrates run?
What's the size of the hospital tank?
"The simplest explanation for some phenomenon is more likely to be accurate than more complicated explanations." -Occam's razor